Sorting Two-Dimensional Nanomaterials by Thickness

ABSTRACT

The present teachings provide, in part, methods of separating two-dimensional nanomaterials by atomic layer thickness. In certain embodiments, the present teachings provide methods of generating graphene nanomaterials having a controlled number of atomic layer(s).

This application is a continuation in part of and claims priority to andthe benefit of application Ser. No. 14/507,240 filed Oct. 6, 2014 whichis a divisional of and claimed priority to and the benefit ofapplication Ser. No. 12/856,348 filed Aug. 13, 2010 and issued as U.S.Pat. No. 8,852,444 on Oct. 7, 2014 which claimed priority to and thebenefit of provisional application Ser. No. 61/234,132, filed on Aug.14, 2009—each of which is incorporated by reference herein in itsentirety.

This invention was made with government support under grant numbersDMR-0520513, EEC-0647560, DMR-0706067, DMR-1006391 and DMR-1121262awarded by the National Science Foundation and grant numbersN00014-09-1-0180 and N00014-09-1-0795 awarded by the Office of NavalResearch. The government has certain rights in the invention.

BACKGROUND OF THE INVENTION

Two-dimensional nanomaterials have emerged as promising materials infield-effect transistors, structurally reinforced composites,chemical/biological sensors, and transparent conductors. Among them,monolayer graphene, a two-dimensional single-atomic layer of carbon, hasgenerated considerable attention as a result of its outstandingelectronic, mechanical, and chemical properties. Since its discovery in2004, monolayer graphene has demonstrated an array of impressiveproperties, such as charge carrier mobilities in excess of 10,000 cm²V⁻¹s⁻¹ (see Zhang et al., Nature, 438: 201 (2005)), the quantum Halleffect at room temperature (see Novoselov et al., Science, 315: 1379(2007)), and a variable band gap depending on adsorbate coverage (seeOhta et al., Science, 313: 951 (2006)). Other two-dimensionalnanomaterials also have been studied, including those derived from boronnitride (BN), transition metal dichalcogenides, graphite oxide, and thehigh temperature superconductor Bi₂Sr₂CaCu₂O_(x). Further, thesemiconducting properties of single flakes of molybdenum disulfide(MoS₂) and graphene oxide have been exploited in field-effecttransistors.

Despite the technological potential of two-dimensional nanomaterials,methods of synthesizing and purifying them are in their infancy. Themost common of these methods, known as micromechanical cleavage,involves drawing a layered crystallite such as graphite over a substrateof interest leaving thin crystallites on the surface (see Novoselov etal., Proc. Nat. Acad. Aci. U.S.A., 102: 10451 (2005)). Althoughmicromechanical cleavage can produce samples of high crystal quality, ithas several disadvantages. First, it is difficult to control theposition at which crystallites will be placed; consequently,considerable effort is required to locate them. Second, cleavage doesnot provide control over the thickness of flakes produced, resulting ina limited number of atomically thin crystallites with the majority beingtens of nanometers thick. Third, the prospects for large scaleproduction of graphene and other crystallites through micromechanicalcleavage are unfavorable.

Other groups have studied epitaxial growth of two-dimensionalnanomaterials on various substrates. For example, graphene can be growndirectly on metal surfaces or through thermal decomposition of SiC (seeBerger et al., Science, 312: 1191 (2006)). However, while theseepitaxial graphene samples have the benefit of spanning large areas,full control over the thickness of the resulting crystallites remains achallenge. Moreover, because epitaxial synthesis can occur only onsuitable growth substrates, methods of transferring crystallites toother substrates are required for practical applications.

Solution-based methods represent a third route to two-dimensionalnanomaterials and can offer several significant advantages over the twoapproaches described above. First, the desired two-dimensionalnanomaterials often can be generated from inexpensive and readilyavailable starting materials. Second, solution-phase techniques do notrequire transfer from the growth substrate, and can employ existingtechnologies for scaling up to large volume processing. Several of thesemethods involve intercalation of graphite and transition metaldichalcogenide crystallites followed by sonication or rapid heating togenerate thin flakes (see Viculis et al., J. Mater. Chem., 15: 927(2005); Yu et al., J. Phys. Chem. C, 111: 7565 (2007); and Joensen etal., Mater. Res. Bull., 21: 457 (1986)). Yet, because of the oftenviolent reactions between the intercalation compounds and water or othersolvents, the resulting crystallites usually are at least partiallyoxidized or otherwise have defect sites which impair their properties(see Li et al., Science, 319, 1229 (2008)).

With respect to the production of monolayer graphene, several groupshave explored exfoliating functionalized graphite, such as graphiteoxide and graphite fluoride. Unlike pristine graphite, graphite oxide ishydrophilic, and individual graphene oxide layers can be dispersedreadily into water. However, graphene oxide is insulating. To regaintheir electrical conductivity, the exfoliated functionalized graphitematerials must be chemically reduced. Despite these treatments, theelectronic properties of reduced graphene oxide remain different fromthose of pristine graphene (see e.g., Tung et al., Nature Nanotech., 4:25 (2009)). Furthermore, while it is possible to generate monolayergraphene oxide by ensuring that graphite is sufficiently oxidized, it isunlikely that bilayer graphene oxide (or n-layer graphene oxide) couldbe formed preferentially through controlled oxidation. Graphenenanomaterials have diverse properties depending on the number of layers.For example, monolayer graphene is a 0 eV bandgap semiconductor. Bilayergraphene, on the other hand, has been shown to have a tunable bandgap inthe infrared. Meanwhile, trilayer graphene is a semimetal whose bandoverlap can be controlled by an applied electric field.

Accordingly, there is a need in the art for methods of preparing andpurifying two-dimensional nanomaterials with controlled number oflayers. In particular, there is a need in the art for methods ofpreparing and purifying graphene nanomaterials with controlled number oflayers, including methods of preparing monolayer graphene and isolatingit from other graphene nanomaterials having two or more layers. Inaddition, there is a need in the art for methods that enable effectivedispersion of graphite or graphene in a fluid medium, particularly inwater, such that the dispersion can remain stable for an extended periodof time.

SUMMARY OF THE INVENTION

In light of the foregoing, the present teachings provide one or moremethods and/or compositions related to generating nanomaterials havingcontrolled thickness or number of atomic layers, which methods andcompositions can overcome various deficiencies and shortcomings of theprior art, including those outlined above.

In one aspect, the present teachings can be directed to sortingtwo-dimensional (planar) nanomaterials by atomic layer thickness.Specifically, a polydisperse population of planar nanomaterials which ispolydisperse at least with respect to thickness can be first contactedwith one or more surface active components to provide a nanomaterialcomposition. In various embodiments, the nanomaterial composition is astable dispersion of the nanomaterials in water, in which thenanomaterials are dispersed effectively by the one or more surfaceactive components. The one or more surface active components can beselected for their ability to associate differentially with thenanomaterials of different thickness such that individual nanomaterialcrystallite or flake of different thickness, upon association with thesurface active components, can exhibit different buoyant densities in afluid medium. Separation by buoyant density subsequently can beaccomplished by, but is not limited to, density gradientultracentrifugation, after which physically separated nanomaterials,grouped according to atomic layer thickness, can be recovered.

Generally, density gradient ultracentrifugation (DGU) involvesintroducing the dispersion into a density gradient medium, that is, afluid medium that includes a density gradient. The density gradient caninclude a linear gradient including three or more layers of differentdensities. Once introduced, the fluid medium can be agitated, forexample, by ultracentrifugation, to allow separation of thenanomaterials by thickness along the density gradient. After sufficientagitation, nanomaterials of different thickness are allowed to settleinto a plurality of separation fractions, where at least one of theseparation fractions is enriched with nanomaterials of a specificthickness. For example, a first separation fraction can be enriched withmonolayer nanomaterials, a second separation fraction can be enrichedwith bilayer nanomaterials, a third separation fraction can be enrichedwith trilayer nanomaterials, and so on. The separation fractions can bevisibly distinguishable among each other by human eye, or can bedistinguishable outside the visible spectrum by various light scatteringor spectroscopic methods. For example, two or more separation fractionscan be distinguishable by different colors and/or different shades of aparticular color in the visible spectrum. Further, the two or moreseparation fractions can be separated from each other by a layer offluid medium in which only a negligible amount of nanomaterials ispresent. For separation fractions that are enriched with monolayer,bilayer, and/or trilayer nanomaterials, the mean thickness of thenanomaterials in such enriched separation fractions can be expected tobe less than the mean thickness of the nanomaterials in the startingnanomaterial composition, which includes a non-negligible amount ofnanomaterials having four layers or more. For example, the meanthickness of the nanomaterials in the starting nanomaterial compositioncan be about 5 nm or greater, and the mean thickness of thenanomaterials in an enriched separation fraction can be between about 1nm and 3 nm.

As used herein, the “mean thickness” is the average thickness ofnanomaterials in a sample otherwise known as the arithmetic mean.Typically, an enriched separation fraction also can have a modethickness that is less than the mode thickness of the nanomaterials inthe starting nanomaterial composition. As used herein, the “modethickness” is the thickness with the highest frequency in a sample. Forexample, the mode thickness of the nanomaterials in an enrichedseparation fraction can be less than 2 nm, whereas the mode thickness ofthe nanomaterials in the polydispersion population can be 4 nm orgreater.

A single separation cycle according to the present methods often leadsto enrichment that is satisfactory for most applications. Accordingly,following one separation cycle, one or more separation fractions can becollected from the density gradient and used for various applications.However, performing one or more additional sorting or separation cyclescan improve the quality of the separation and provide increasinglyenriched separation fractions.

In another aspect, the present teachings relate to producing aqueousdispersions of two-dimensional (planar) hydrophobic nanomaterials. Incontrast to the prior art, the present teachings provide stable aqueousdispersions of two-dimensional hydrophobic nanomaterials withoutchemical modification such as oxidation. Instead, stable aqueousdispersions are obtained by providing the hydrophobic nanomaterials incomposition with one or more surface active components described herein,in particular, surface active components having one or more planarorganic groups. Without wishing to be bound by any particular theory, itis believed that one or more surface active components described hereincan encapsulate individual flakes of nanomaterials and allow a largeamount of the nanomaterials to be effectively dispersed in water. Forexample, aqueous dispersions having a minimum concentration of 40 μg/mLof nanomaterials according to the present teachings can remain stablefor weeks without visible aggregation.

Other objects, features, and advantages of the present teachings will bemore fully understood from the following figures, description, examples,and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

It should be understood that certain drawings are not necessarily toscale, with emphasis generally being placed upon illustrating theprinciples of the present teachings. The drawings are not intended tolimit the scope of the present teachings in any way.

FIG. 1A is a schematic illustration of the solution-phase exfoliationprocess according to the present teachings.

FIG. 1B is a schematic illustration of a monolayer two-dimensionalnanomaterial encapsulated by an ordered monolayer of surface activecomponents on each side.

FIG. 1C is a photograph showing a centrifuge tube containing graphenenanomaterials after one iteration of density gradientultracentrifugation (DGU) according to the present methods. Theconcentrated graphene was diluted by a factor of 40 to ensure that allgraphene bands could be clearly resolved in the photograph. Lines markthe positions at which sorted graphene fractions f4, f10, f16, f22, andf28 were extracted within the centrifuge tube.

FIG. 2A is a histogram comparing the mean flake thickness (calculatedusing AFM images) for sedimented, concentrated, and DGU fraction f4graphene dispersions.

FIG. 2B is a histogram plotted by relative frequency (mode thicknessscaled to unity) comparing the mean flake thickness (calculated usingAFM images) for DGU fractions f4, f16, and f28.

FIG. 3A is a schematic illustration of a buoyant density model forsurfactant-encapsulated few-layer graphene nanomaterials in which aflake of thickness N is coated by a surfactant with a packing density σand an effective thickness t_(A) and a hydration layer of thicknesst_(H).

FIG. 3B shows the fit between the buoyant density model and theexperimental data. The uncertainty in graphene flake thickness was takenas the full-width at half maximum (FWHM) of the flake thicknessdistribution.

FIG. 4A shows representative Raman spectra of sorted graphene flakesfrom fractions f4, f16, and f28 on SiO₂ in the D and G band region withthe intensity of the G band normalized to unity.

FIG. 4B shows the 2D band of the spectra in FIG. 4A, as well asfractions f10 and f22, with the same G band normalization.

FIG. 4C plots the ratio of 2D and G band intensity I(2D)/I(G) andFWHM(2D) as a function of the mean graphene thickness. Triangles andsquares represent I(2D)/I(G) and FWHM(2D), respectively. Open symbolsmark values obtained from the concentrated graphene dispersion. Solidsymbols mark values obtained from DGU-processed fractions.

FIG. 5A shows the effect of annealing on the transmittance and sheetresistance of graphene transparent conductors produced from theconcentrated and f4 graphene dispersions. Triangles and circlesrepresent the films before and after annealing for two hours at 250° C.in air, respectively. Lines are drawn between points to aid the eye.

FIG. 5B shows the sheet resistance and transmittance of pristine (notannealed) graphene transparent conductors made from various sedimenteddispersions. Lines are drawn between points to aid the eye.

FIG. 6A plots the transmittance of graphene transparent conductorsproduced from sedimented, concentrated, f4, f16, and f28 dispersions asa function of their sheet resistance at wavelengths of 550 nm. Lines aredrawn between points to aid the eye.

FIG. 6B plots the transmittance of graphene transparent conductorsproduced from sedimented, concentrated, f4, f16, and f28 dispersions asa function of their sheet resistance at wavelengths of 1000 nm. Linesare drawn between points to aid the eye.

FIGS. 7A-C. Schematic illustration of the MoS₂ exfoliation process andbuoyant density model. (A) Schematic of the MoS₂ exfoliation process inaqueous solution. In particular, MoS₂ flakes are exfoliated anddispersed by Pluronic F68 during tip ultrasonication. The brown andpurple atoms are sulfur and molybdenum, and the green and blue spheresare PEO and PPO chains, respectively. (B) Buoyant density model forF68-encapsulated MoS₂ in aqueous solution, where N is the number of MoS₂layers, t_(A) is the anhydrous layer thickness, t_(H) is the hydrationshell thickness, and σ is the packing density. (C) Buoyant density modelas a function of MoS₂ flake thickness. Lines represent scenarios whereMoS₂ is encapsulated with F68 and sodium cholate (SC), respectively. Thearea enclosed by the two black lines indicates the possible buoyantdensity range that depends on the surface coverage of Pluronic F68 onMoS₂. Isopycnic DGU separation of MoS₂ is only possible when thesurfactant-encapsulated MoS₂ nanosheets have a buoyant density below thedensity limit imposed by the density gradient medium (dashed-line).

FIGS. 8A-C. Digital images of the experimental procedure. (A) Images ofthe concentration step for MoS₂ nanosheets. After ultrasonication, theMoS₂ dispersion is placed on top of 60% w v⁻¹ iodixanol as a stepgradient and then ultracentrifuged at 32 krpm for 24 hours.Subsequently, 60% w v⁻¹ iodixanol is injected to separate theconcentrated MoS₂ nanosheets from the aggregates, and then extracted.The dispersion, gradient, and injection solution all contain 2% w v⁻¹F68. (B) Image of MoS₂ bands in an ultracentrifuge tube after the firstiteration of density gradient ultracentrifugation (DGU). Theconcentrated MoS₂ solution was diluted by a factor of eight prior toultracentrifugation to reveal the position of each band more clearly.(C) Image of the ultracentrifuge tubes after the second iteration ofDGU. Fractions from the well-defined bands (f7, f17, and f27) and therelatively wider bands (f9, f13, and f23) from the first iteration arecollected and used for the second iteration. The fractions from thedashed region are used for characterization.

FIGS. 9A-D. Atomic structure of MoS₂ before and after DGU. (A) Schematicillustration of the 2H semiconducting crystal structure of MoS₂ shownfrom out-of-plane and perspective view (Blue: Mo, Brown: S). (B) FastFourier Transform of the STEM images. (C), (D) HAADF-STEM images of MoS₂flakes before and after DGU, respectively. The inset image shows themagnified STEM image after DGU. The blue and brown spheres indicate theposition of Mo and S atoms, respectively (scale bar=0.5 nm).

FIGS. 10A-C. Characterization of thickness and area distribution. (A)Atomic force microscopy (AFM) images of MoS₂ nanosheets from f7 and f17on a SiO₂ substrate and the corresponding height profiles along thedashed lines (scale bar=100 nm). (B) Flake thickness and (C) flake areahistograms for f7, f17, and f27 fractions obtained from the AFM images.

FIGS. 11A-D. Buoyant density analysis and optical properties. (A)Experimental data (squares) are plotted with the buoyant density modelusing a surface coverage variation from 10% to 100% (black lines). Thesurface coverage of F68 on the MoS₂ surface determined from theexperimental data, which corresponds to approximately 42.5%, is alsoshown. (B) Optical absorbance spectra of fractions f7, f17, and f27, andthe MoS₂ dispersion before separation. (C) Raman spectra of eachfraction showing the shifts in the in-plane and out-of-plane vibrationalmodes as a function of MoS₂ thickness. (D) Photoluminescence spectra offraction f7 compared to a micromechanically exfoliated monolayer MoS₂.

FIG. 12. Chemical structure of Pluronic F68 showing its hydrophilic PEOand hydrophobic PPO chains. Pluronic F68, a block copolymer dispersantcomposed of a central hydrophobic PPO unit flanked by hydrophilic PEOchains.

FIGS. 13A-B. AFM image (A) of MoS₂ nanosheets from f27 on a SiO₂substrate, and the corresponding height profiles (B) along the dashedline (scale bar=100 nm).

FIGS. 14A-B. Photoluminescence spectra comparison. Optical microscopyimage (A) of micromechanically exfoliated MoS₂ and PL intensitycomparison (B) between micromechanically exfoliated monolayer MoS₂ andsorted MoS₂ (f7) via DGU.

DETAILED DESCRIPTION OF CERTAIN EMBODIMENTS

Throughout the description, where compositions are described as having,including, or comprising specific components, or where processes aredescribed as having, including, or comprising specific process steps, itis contemplated that compositions of the present teachings also consistessentially of, or consist of, the recited components, and that theprocesses of the present teachings also consist essentially of, orconsist of, the recited processing steps.

In the application, where an element or component is said to be includedin and/or selected from a list of recited elements or components, itshould be understood that the element or component can be any one of therecited elements or components or can be selected from a groupconsisting of two or more of the recited elements or components.Further, it should be understood that elements and/or features of acomposition, an apparatus, or a method described herein can be combinedin a variety of ways without departing from the spirit and scope of thepresent teachings, whether explicit or implicit herein.

The use of the terms “include,” “includes,” “including,” “have,” “has,”“having,” “contain,” “contains,” or “containing” should be generallyunderstood as open-ended and non-limiting unless specifically statedotherwise.

The use of the singular herein includes the plural (and vice versa)unless specifically stated otherwise. In addition, where the use of theterm “about” is before a quantitative value, the present teachings alsoinclude the specific quantitative value itself, unless specificallystated otherwise. As used herein, the term “about” refers to a ±10%variation from the nominal value unless otherwise indicated or inferred.

It should be understood that the order of steps or order for performingcertain actions is immaterial so long as the present teachings remainoperable. Moreover, two or more steps or actions may be conductedsimultaneously.

As used herein, a “planar nanomaterial” or a “two-dimensionalnanomaterial” refers to a planar structure having a thickness on theorder of nanometers, generally 100 nm or less, for example, less thanabout 50 nm, usually less than about 10 nm, and in some embodiments,less than about 5 nm thick. The thickness of the present planarnanomaterials can be measured in terms of the number of atomic ormolecular layers, and can have one to about 50 atomic or molecularlayers. For example, the planar nanomaterials of the present teachingscan include monolayer nanomaterials, that is, nanomaterials consistingof a single atomic or molecular layer; bilayer nanomaterials, that isnanomaterials consisting of two atomic or molecular layers; trilayernanomaterials, that is nanomaterials consisting of three atomic ormolecular layers; and few-layer nanomaterials, which refer to planarnanomaterials consisting of four to about ten atomic or molecularlayers. Typically, planar nanomaterials of the present teachings havelarge length-to-thickness and/or width-to-thickness ratio(s). Forexample, a planar nanomaterial of the present teachings can have alength in the range of about 1 μm to 20 μm, in which case, thelength-to-thickness ratio is on the order of 10³ or larger. Inembodiments where the present planar nanomaterials have a large aspectratio (large length-to-width ratio), for example, when the nanomaterialshave a nanoscale width in addition to the nanoscale thickness, thenanomaterials can be referred herein as “nanoribbons.” In otherembodiments, the present planar nanomaterials can be referred herein as“nanosheets” or “nanoflakes” (or simply “flakes”) with the formergenerally having larger length and width dimensions than the latter.

The present teachings can be practiced on various elemental or molecularnanomaterials including those composed of carbon, BN, transition metaldichalcogenides such as WS₂ and MoS₂, and the high temperaturesuperconductor Bi₂Sr₂CaCu₂O_(x). In various embodiments, the presentplanar nanomaterials can include graphene nanomaterials. As used herein,“graphene nanomaterials” include n-layer graphene nanomaterials, whereinn is an integer in the range of 1 to 10, and specifically includemonolayer graphene (n=1), bilayer graphene (n=2), trilayer graphene(n=3), and few-layer graphene (n=4-10) nanomaterials. As understood bythose skilled in the art, monolayer graphene is a one atomic layer (ormonolayer) thick planar sheet of sp²-bonded carbon atoms that aredensely packed in a honeycomb crystal lattice, whereas p-layer graphenenanomaterials (n=2-10) have stacked planar structures consisting of twoto ten graphene sheets. In various embodiments, graphite (e.g.,naturally occurring crystalline flake graphite) can be used as thestarting material for preparing graphene nanomaterials includingmonolayer graphene. However, other forms of graphite including syntheticforms of graphite (e.g., highly ordered pyrolytic graphite (HOPG)) alsocan be used. As understood by those skilled in the art, graphite is athree-dimensional layered material consisting of many (usually hundredsor more of) stacked graphene sheets and has a typical thickness that isgreater than 100 nm. As such, graphene and graphite, as used herein, donot encompass other non-planar allotropes of carbon such as carbonnanotubes which are very different from graphene and graphite not onlyin terms of shape but also physical, chemical, optical, and electronicproperties. While the description and examples herein may referspecifically to graphene and graphite, the present teachings areintended to encompass two-dimensional planar nanomaterials in generalregardless of their composition.

As used herein, a “population” of nanomaterials can include greater thanabout 10⁸, greater than about 10⁹, greater than about 10¹⁰, greater thanabout 10¹¹, greater than about 10¹², greater than about 10¹³, greaterthan about 10¹⁴, greater than about 10¹⁵, greater than about 10¹⁶, orgreater than about 10¹⁷ nanoribbons, nanosheets, or nanoflakes. Further,by weight, a population of nanomaterials can have a mass of about 0.001μg, greater than about 0.01 μg, greater than about 0.1 μg, greater thanabout 1 μg, greater than about 10 μg, greater than about 100 μg, greaterthan about 1 mg, greater than about 10 mg, greater than about 100 mg, orgreater than about 1 g. In certain embodiments of the present teachings,a separation cycle can be used to sort bulk quantities of nanomaterials,for example, populations of nanomaterials that include more than about10¹², more than about 10¹³, more than about 10¹⁴, more than about 10¹⁵,more than about 10¹⁶ or more than about 10¹⁷ nanoribbons, nanosheets, ornanoflakes; or more than about 10 μg, more than about 100 μg, more thanabout 1 mg, more than about 10 mg, more than about 100 mg, or more thanabout 1 gram of nanomaterials by mass.

As used herein, “enrichment” or “enriched” refers to an increase in thestatistical proportion of nanomaterials comprising one or more specificcharacteristics in a fraction (or subpopulation) obtained from a samplepopulation as compared to the sample population as a whole. As describedherein, a nanomaterial subpopulation that is “enriched” according to thepresent teachings by one or more properties, such as thickness, shape,aspect ratio, or combinations thereof, means that the subpopulation(i.e., the enriched population) has a higher percentage of nanomaterialshaving the one or more properties when compared to the startingpopulation (i.e., the mixed population) from which the subpopulation isderived. For example, a starting population of planar nanomaterials canexhibit polydispersity in thickness and can include monolayer, bilayer,trilayer, and few-layer (n≧4) planar nanomaterials. Using methods of thepresent teachings, a subpopulation derived from the polydispersepopulation can be enriched with monolayer, bilayer, and/or trilayerplanar nanomaterials and as a result of which, have a reduced meanthickness compared to the starting population.

Various methods have been used to different degrees of success forseparating carbon nanotubes by one or more characteristics such aschirality, diameter, and electronic type. However, the extension ofseparation methods for carbon nanotubes to graphene nanomaterials by oneor more selected properties has not been described in the literature.Because of their geometrical differences (planar versus tubular) anddifferent properties such as surface energy, optical properties, andelectronic properties, graphene can be expected to respond verydifferently to a particular separation method when compared to carbonnanotubes. For example, to the inventors' knowledge, there has been noreported method for separating graphene nanomaterials by thickness thatallows isolation of monolayer graphene from bilayer, trilayer, and/orfew-layer graphene nanomaterials. In addition, when graphenenanomaterials are generated in situ from graphite, in particular byexfoliation in aqueous systems, further challenges exist with regard todispersing the highly hydrophobic graphite at sufficiently highconcentrations.

Accordingly, in one aspect, the present teachings provide asolution-phase method for generating two-dimensional planarnanomaterials from three-dimensional crystalline materials. For example,using methods of the present teachings, two-dimensional planarnanomaterials can be generated from three-dimensional crystallinematerials including, but not limited to, graphite, MoS₂, and BNcrystallites. The resulting two-dimensional planar nanomaterialssubsequently can be separated by thickness using density gradientultracentrifugation (DGU) as described in further detail below.

According to the present teachings, the starting three-dimensionalmaterials are first exfoliated into two-dimensional planar nanomaterialshaving ten or less atomic or molecular layers. More specifically, in thefirst stage of the exfoliation process, the three-dimensional startingmaterials are added to a fluid medium containing one or more surfaceactive components to provide a dispersion. The dispersion containing thestarting materials and the surface active components is then subjectedto a non-thermal, non-oxidative agitation process to exfoliate thethree-dimensional materials into two-dimensional nanomaterials. Morespecifically, ultrasonic agitation (or ultrasonication) can be used toinduce effective exfoliation.

In various embodiments, the three-dimensional starting materials can befrom a natural source. For example, graphite and MoS₂ (in the form ofmolybdenite) can be mined from ores. In certain embodiments, thethree-dimensional layered materials can be pristine (i.e., asnaturally-occurring or as-synthesized) and have not been subjected topost-extraction or post-synthesis treatment (e.g., thermal treatment ata temperature above 100° C. and/or chemical modification such astreatment under oxidative (acidic) and/or reducing conditions). Forexample, the starting materials can be pristine graphite flakes, whichare to be differentiated from graphite oxide, graphite fluoride, orother functionalized forms of graphite. In addition, to increase theyield of exfoliated nanomaterials, the starting materials can beprovided in powder form, although in certain embodiments, bulk crystalsalso can be used.

It has been found that a variety of surface active components areeffective at dispersing both the three-dimensional starting materialsand the exfoliated two-dimensional planar nanomaterials. For example,anionic surfactants such as bile salts and alkali salts of alkyl sulfateand alkyl benzene sulfonate; and cationic surfactants such as quaternaryammonium salts have been found effective and useful in accordance withthe present teachings. In addition, polymers including cyclic groups inthe backbone and/or the side chains such as polyvinylpyrrolidone andcarboxymethylcellulose; non-ionic block copolymers of oxyethylene andoxypropylene; and polymers including one or more polyoxyethylene chainssuch as polyoxyethylene alkylphenyl ethers and polyoxyethylene sorbitanalkyl ethers have been found useful.

In certain embodiments, surface active components that include one ormore planar organic groups can be particularly useful both foreffectively dispersing the starting materials and subsequently enablingseparation of the nanomaterials by thickness. Without wishing to bebound by any particular theory, it is believed that surface activecomponents which have one or more planar organic groups can intercalatebetween the layers of the three-dimensional layered materials moreeffectively, thereby promoting exfoliation and increasing the yield oftwo-dimensional planar nanomaterials, in particular, monolayernanomaterials. Accordingly, in certain embodiments, the one or moresurface active components can include an amphiphilic non-polymericcompound having a planar hydrophobic core and one or more hydrophilicgroups. For example, the one or more surface active components caninclude a compound having a cyclic (e.g., carbocyclic) core and one ormore charged groups, particularly, a benzene group or a sterane groupand one or more anionic groups selected from hydroxyls, carboxylates,sulfates, sulfonates, and combinations thereof. In particularembodiments, the one or more surface active components can include oneor more bile salts and/or an alkali salt of linear alkylbenzenesulfonate such as sodium dodecylbenzenesulfonate. Bile salts canbe more broadly described as a group of molecularly rigid and planaramphiphiles with one or more charged groups opposing a hydrophobic face.Examples of bile salts include salts (e.g., sodium or potassium salts)of conjugated or unconjugated cholates and cholate derivatives includingdeoxycholates, chenodeoxycholates, taurodeoxycholates,glycochenodeoxycholates, ursodeoxycholates, and glycoursodeoxycholates.In certain embodiments, the one or more surface active components caninclude a polymer having one or more cyclic groups in its backboneand/or side chains. For example, polyvinylpyrrolidones over a largemolecular weight range (e.g., between about 5 kDa and about 1500 kDa)have been found useful. It also has been discovered that sodiumcarboxymethylcelluose is particularly effective as a surface activecomponent for dispersing hydrophobic two-dimensional nanomaterials,despite the fact that the glucose rings in the polysaccharide can assumeboth planar and non-planar configurations.

Other useful surface active components include alkyl sulfates such assodium hexyl sulfate, sodium octyl sulfate, sodium decyl sulfate, sodiumundecyl sulfate, sodium dodecyl sulfate, and lithium dodecyl sulfate;quaternary ammonium salts such as dodecyltrimethylammonium bromide,myristyltrimethylammonium bromide, hexadecyltrimethylammonium bromide,hexadecyltrimethylammonium chloride, and hexadecyltrimethylammoniumhydrogen sulfate; polyoxyethylene alkylphenyl ethers such as Triton®X-100; polyoxyethylene sorbitan alkyl ethers such as Tween® 20 andTween® 85; poloxamers (or non-ionic triblock copolymers of oxyethyleneand oxypropylene known under the trade name Pluronic®) which can berepresented by the general formula HO(C₂H₄O)_(a)(C₃H₆O)_(b)(C₂H₄O)_(a)H,wherein a and b are integers in the range of 10 to 300; and non-ionictetrafunctional block copolymers of oxyethylene and oxypropylene knownunder the trade name Tetronic®.

State-of-the-art exfoliation methods for preparing nanomaterials oftenare performed in expensive organic solvents due to the highlyhydrophobic nature of most planar nanomaterials and their startingmaterials. By using the surface active components described herein, itwas surprisingly found that highly hydrophobic materials such asgraphite and graphene can be uniformly dispersed in water at highconcentrations. For example, for the initial exfoliation step, graphitecan be effectively dispersed at concentrations higher than about 50mg/mL in an aqueous solution containing the surface active components.The fact that the present methods can be practiced with a highconcentration of the starting materials help ensure a high throughput ofthe process. In addition, aqueous dispersions of graphene in compositionwith one or more surface active components described herein can have agraphene concentration higher than about 0.10 mg/mL, higher than about0.20 mg/mL, higher than about 0.30 mg/mL, higher than about 0.40 mg/mL,higher than about 0.50 mg/mL, higher than about 0.60 mg/mL, higher thanabout 0.70 mg/mL, higher than about 0.80 mg/mL, higher than about 0.90mg/mL, or higher than about 0.95 mg/mL and remain stable (e.g., withoutvisible aggregation) for at least two weeks, for at least three weeks,for at least one month, or for at least two months. Stable aqueousdispersions of MoS₂ and BN also can be obtained similarly with one ormore surface active components described herein.

In embodiments where the present methods are used to generate graphenenanomaterials, planar surface active components such as sodium cholate,sodium carboxymethylcellulose, and other surface active componentsincluding one or more planar organic groups can be used. Both thestarting layered materials (i.e., graphite) and the exfoliatednanomaterials (i.e., graphene nanomaterials) can form a complex with thesurface active components. According to the present methods, sodiumcholate and other surface active components are not intended tochemically modify or functionalize the starting materials or theexfoliated nanomaterials. Instead, the one or more surface activecomponents typically are selected to ensure non-covalent associationwith the materials, whether it is by ionic interaction, π-π orbitalinteraction, hydrogen bonding, Van Der Waals interaction, orcombinations thereof. In some embodiments, the materials can beconsidered as being “encapsulated” by the surface active components. Asused herein, “encapsulate,” “encapsulated,” or “encapsulating” refers tonon-covalent association with a target. For example, the one or moresurface active components can arrange themselves as a sheet and cover atleast 50% of one or more surfaces of the target. In certain embodiments,the one or more surface active components can form an ordered layer oneach side of the target, yet not be present at one or more edges of thetarget.

FIG. 1A is a schematic illustration of the solution-phase exfoliationprocess according to the present teachings. In particular, theexfoliation process can be performed in an aqueous solution containingone or more surface active components. For example, a three-dimensionallayered material such as graphite flakes can be combined with a surfaceactive component such as sodium cholate in an aqueous solution. Hornultrasonication then can be used to exfoliate the three-dimensionalgraphite flakes into graphene nanomaterials that are encapsulated by thesurface active components. FIG. 1B provides a schematic illustration ofa monolayer nanoflake (e.g., monolayer graphene) encapsulated by anordered monolayer of surface active components (e.g., sodium cholate) oneach side.

Following ultrasonication, the sonicated dispersion can includetwo-dimensional nanomaterials as well as three-dimensional materials.Among the two-dimensional nanomaterials, there can be a polydispersepopulation of monolayer nanomaterials, bilayer nanomaterials, trilayernanomaterials, and higher-order few-layer nanomaterials. Beforeseparating the two-dimensional nanomaterials by thickness, thethree-dimensional materials can be removed and/or the sonicateddispersion can be concentrated to improve the quality of the separationprocess.

For example, the sonicated dispersion can be subjected to sedimentationcentrifugation. In various embodiments, the sonicated dispersion can becentrifuged at about 21,000 relative centrifugal force for severalminutes to remove fast sedimenting large crystallites from thedispersion. The supernatant then can be recovered to form a basedispersion. The crystallites in the base dispersion can comprise aconcentration of at least about 0.05 mg/mL and be stable. For example,the crystallites in the recovered base dispersion may not show signs ofreaggregation for at least two weeks following their initial dispersion.

Following the procedures described above, a well-dispersed aqueoussolution of two-dimensional nanomaterials can be obtained. Because thenanomaterials provided by the present teachings are produced without anycovalent chemical modification, the nanomaterials of the presentteachings can offer greater crystallinity and environmental stabilitythan those obtained using prior art methods such as intercalation.Aqueous dispersions of the present two-dimensional nanomaterials can beused for controlled deposition using methods previously developed todeposit other nanomaterials such as carbon nanotubes and inorganicnanowires. Such deposition methods include dielectrophoresis (see R.Krupke et al., Science 301, 344 (2003)), self-assembled monolayermediated adhesion (see M. Burghard et al., Adv. Mater. 10, 584 (1998)),and Langmuir-Blodgett assembly (see X. Li et al., J. Am. Chem. Soc. 129,4890 (2007)). Atomic force microscopy (AFM) images of thin filmsdeposited onto SiO₂-capped Si wafers from base dispersions according tothe present methods confirm the presence of crystallites withthicknesses ranging from about 1 nm to about 10 nm.

For further refinement, the base dispersions described above can beconcentrated by ultracentrifugation in a step gradient. Morespecifically, a base dispersion can be layered on top of a denseunderlayer, e.g., a dense underlayer of 60% w/v iodixanol, andultracentrifuged in the resulting step gradient. Ultracentrifugationcauses the nanomaterials in the base dispersion to sediment into thestep gradient formed at the interface between the two layers, producinga concentrated band of two-dimensional nanomaterials that can be removedby fractionation. In addition to producing a concentrated dispersion ofcrystallites, ultracentrifugation in a step gradient also removes thickcrystallites (including nanomaterials consisting of more than tenlayers) whose buoyant density exceeds the density of the step gradient.

To provide two-dimensional nanomaterials having a controlled thickness(or number of atomic layer), the base dispersion or the concentrateddispersion can be subjected to density gradient ultracentrifugation(DGU). During DGU, the differences in the buoyant density of thetwo-dimensional nanomaterials and that of the surrounding medium drivethe two-dimensional nanomaterials to their respective isopycnic points,where the buoyant density of a particular nanomaterial crystallitematches that of the surrounding medium. In particular, because monolayernanomaterials, bilayer nanomaterials, trilayer nanomaterials, andhigher-order few-layer nanomaterials have different buoyant densitiesupon association with the present surface active components,ultracentrifugation in a density gradient will cause the encapsulatednanomaterials to separate by thickness into distinct often visible bands(or separation fractions) of nanomaterials. For example, it wasempirically found that the buoyant density of graphene nanomaterialsincreases with thickness when centrifuged in composition with sodiumcholate; accordingly, the topmost separation fraction is expected to beenriched with monolayer graphene. To illustrate, after the sedimentationand/or the concentration step(s), the nanomaterial dispersion caninclude less than about 30% monolayer nanomaterials among all thegraphene nanomaterials in the dispersion. After one iteration of the DGUprocess, the topmost separation fraction can include at least about 50%,at least about 60%, at least about 70%, at least about 80%, or at leastabout 90% monolayer nanomaterials among all the graphene nanomaterialsin that topmost separation fraction.

Generally, density gradient ultracentrifugation uses a fluid medium witha predefined variation in its density as a function of position within acentrifuge tube or compartment (i.e., a density gradient). Fluid mediauseful with the present teachings are limited only by nanomaterialaggregation therein to an extent precluding at least partial separation.Accordingly, aqueous and non-aqueous fluids can be used in conjunctionwith any substance soluble or dispersible therein, over a range ofconcentrations, so as to provide the medium a density gradient for usein the separation techniques described herein. Such substances can beionic or non-ionic, non-limiting examples of which include inorganicsalts and alcohols, respectively. Such a medium can include a range ofaqueous iodixanol concentrations and the corresponding gradient ofconcentration densities. As understood by those skilled in the art,aqueous iodixanol is a common, widely used non-ionic density gradientmedium. However, other media can be used in methods of the presentteachings, as would be understood by those skilled in the art.

More generally, any material or compound stable, soluble or dispersiblein a fluid or solvent of choice can be used as a density gradientmedium. A range of densities can be formed by dissolving such a materialor compound in the fluid at different concentrations, and a densitygradient can be formed, for instance, in a centrifuge tube orcompartment. More practically, with regard to choice of medium, thetwo-dimensional nanomaterials in composition with the surface activecomponents should be soluble, stable or dispersible within thefluids/solvent or resulting density gradient. Likewise, from a practicalperspective, the maximum density of the gradient medium, as determinedby the solubility limit of such a material or compound in the solvent orfluid of choice, should be at least as large as the buoyant density ofthe nanomaterial-surface active component complexes for a particularmedium. Accordingly, any aqueous or non-aqueous density gradient mediumcan be used provided that the nanomaterials are stable; that is, do notaggregate to an extent precluding useful separation. Alternatives toiodixanol include inorganic salts (such as CsCl, Cs₂SO₄, KBr, etc.),polyhydric alcohols (such as sucrose, glycerol, sorbitol, etc.),polysaccharides (such as polysucrose, dextrans, etc.), other iodinatedcompounds in addition to iodixanol (such as diatrizoate, nycodenz,etc.), and colloidal materials (such as Percoll®). Other parameterswhich can be considered upon choice of a suitable density gradientmedium include the diffusion coefficient and the sedimentationcoefficient, both of which can determine how quickly a gradientredistributes during centrifugation. Generally, for more shallowgradients, a larger diffusion coefficient and a smaller sedimentationcoefficient are desired.

It has been discovered that the point at which the encapsulatednanomaterials are introduced into the density gradient in the fluidmedium can be important to the quality of the separation. In someembodiments, the encapsulated nanomaterials are introduced into thedensity gradient at a density that is expected to be greater than thebuoyant density of any of the encapsulated nanomaterials. In someembodiments, the encapsulated nanomaterials are introduced into thedensity gradient at a density that is expected to be lower than thebuoyant density of any of the encapsulated nanomaterials.

In certain embodiments, the nanomaterials (e.g., the concentrateddispersion) can be injected at the bottom of the linear density gradientand centrifuged. Under such condition, the nanomaterials are expected tomove upwards to their isopycnic points and settle into multiple bands orseparation fractions of nanomaterials. The nanomaterials in theseseparation fractions can be sufficiently monodisperse or selective formost applications, and therefore, can be collected and used ‘as is’(optionally after removal of the surface active components) forprocessing into various composites and devices.

In certain embodiments, it can be desirable to purify further theseparation fractions to improve their selectivity by performingadditional iterations of the present methods. Specifically, a separationfraction can be provided in a composition with the same surface activecomponent system or a different surface active component system, and thecomposition can be contacted with the same fluid medium or a differentfluid medium, where the fluid medium can have a density gradient that isthe same or different from the fluid medium from which the separationfraction was obtained. In certain embodiments, fluid medium conditionsor parameters can be maintained from one separation to another. In otherembodiments, at least one iterative separation can include a change ofone or more parameters including the identity of the surface activecomponent(s), medium identity, medium density gradient, and/or mediumpH, as well as the duration and the rotational speed of thecentrifugation process, with respect to one or more of the precedingseparations. In certain embodiments, the surface active component(s)encapsulating the nanomaterials can be modified or changed betweeniterations, allowing for even further refinement of separation.Separation fractions isolated after each separation can be washed beforefurther complexation and centrifugation steps are performed.

For example, after a first separation cycle where the nanomaterials(e.g., the concentrated dispersion) are injected at the bottom of thelinear density gradient and centrifuged, one or more resultingseparation fractions can be collected and be subjected to a seconditeration of the DGU process. For this second iteration, the separationfractions can be loaded at the top of a second density gradient forcingthe graphene nanomaterials to move downward in the centrifuge tube totheir respective isopycnic points. This second DGU iteration can helpremove slow-moving, low buoyant density materials that did not reachtheir isopycnic points in the first iteration. Again, afterultracentrifugation, the nanomaterials are expected to settle intomultiple bands or separation fractions, where the separation fractionsresulting from the second DGU process can have higher monodispersity inthickness compared to the separation fraction(s) resulting from thefirst DGU process.

The selectivity of the fraction(s) collected can be confirmed by variousanalytical methods including optical absorbance, Raman spectroscopy,transmission emission spectroscopy (TEM), fluorescence spectroscopy,atomic force microscopy, and other methods known in the art.

Nanomaterials provided by the present methods can be highly monodispersein thickness. For example, the present methods allow production ofgraphene nanomaterials having a high percentage of monolayer graphene,bilayer graphene, and/or trilayer graphene, and substantially free offew-layer (n≧4) graphene nanomaterials. In addition, because the presentmethods generally do not include any thermal or chemical (e.g.,oxidative and/or reductive) treatment, nanomaterials provided by thepresent methods can be considered pristine, that is, they have not beenoxidized, reduced, and/or otherwise chemically modified in any way. Forexample, monolayer graphene provided by the present methods generally issubstantially defect-free. Compared to graphene nanomaterials which areprepared from reduction of exfoliated graphite oxide, the presentgraphene nanomaterials generally have better electronic properties,specifically, in terms of higher electrical conductivity (or lower sheetresistance).

The nanomaterials according to the present teachings can be processedinto various composites and devices. For example, the presentnanomaterials can be prepared as an aqueous dispersion in compositionwith sodium cholate and/or other surface active components and processedvia various solution-phase techniques known in the art such as spraycoating, drop casting, spin coating, dip coating, and printing. Inaddition, thin films of nanomaterials can be prepared by filtering ananomaterial dispersion under vacuum (i.e., by vacuum filtration)through a porous membrane as known by those skilled in the art. Filmsprepared from sorted nanomaterials according to the present teachingscan have various desirable properties over those prepared from unsortednanomaterials. For example, films obtained from graphene nanomaterialshaving a high percentage of monolayer graphene can exhibit high opticaltransmittance (e.g., >50%) in a wide transmittance window (from ˜300 nmto 3300 nm) and a low sheet resistance (e.g., 5 kΩ/or less). Theelectrical conductivity of the films can be further improved byannealing the films at relatively low temperature (<300° C.), reducingthe sheet resistance to about 2 kΩ/or less, for example, about 1.5kΩ/with a transmittance of about 65% in the visible range. Bycomparison, films produced from polydisperse graphene/graphitenanomaterials using conventional sedimentation-based centrifugationtechniques typically exhibit a sheet resistance of greater than or about10 kΩ/with a transmittance of about 60% in the visible range.

As discussed above, the present invention can be directed to the sortingof two-dimensional transition metal dichalcogenides (TMDs). (See, e.g.,paragraphs [0045], [0049] and [0109]-[0113].) Without limitation,representative of such embodiments, consider the following. Molybdenumdisulfide (MoS₂), one of the TMDs, has been studied with great interestfor a wide range of applications due to its unique electronic, optical,and catalytic properties. The bulk MoS₂ crystal is a semiconductor witha 1.2 eV indirect bandgap and consists of covalently bonded S—Mo—Sstoichiometric layers that interact with neighboring layers via therelatively weak van der Waals interaction. When isolated as a singlestoichiometric layer, MoS₂ shows strong visible photoluminescence due tothe emergence of a 1.9 eV direct bandgap at the K point of the hexagonalBrillouin zone. In order to fully understand and exploit the uniqueproperties of single-layered MoS₂, many production methods have beendeveloped including micromechanical, chemical, and surfactant-assistedliquid-phase exfoliation, in addition to growth via chemical vapordeposition. While the micromechanical cleavage technique producessingle- or few-layered MoS₂ with high structural quality, this methodlacks sufficient scalability for practical applications. On the otherhand, solution-phase exfoliation of single-layered MoS₂ can be achievedby lithium intercalation, although this process drives a phasetransition to the metallic 1T-MoS₂ structure, thus necessitatingsubsequent thermal treatments in an attempt to recover thesemiconducting 2H—MoS₂ phase. However, complete semiconducting phaserecovery has not yet been demonstrated, and the presence of the residualmetallic phase can have detrimental effects, especially in electronicapplications. Alternative liquid exfoliation methods can avoid themetallic 1T-MoS₂ phase transition, but typically yield a range of MoS₂flake thicknesses. Lastly, ultrathin MoS₂ growth by chemical vapordeposition requires high temperature processing and subsequent transferfrom the growth substrate, which is arguably more cumbersome thansolution-based approaches.

Furthermore, as discussed above, the present invention provides analternative solution-based route for preparing structurally pristine,ultrathin MoS₂ nanosheets via isopycnic density gradientultracentrifugation (DGU). To more specifically assess the applicabilityof DGU to MoS₂ nanosheets, and with reference to paragraph [0085], thefollowing geometrical buoyant density model was used for SC-encapsulatedMoS₂:

${\rho (N)} = \frac{{\rho_{S}N} + {2\; m_{surf}\sigma} + {2\; \rho_{H_{2}O}t_{H}}}{{\left( {N + 1} \right)t_{{MoS}_{2}}} + {2\; t_{A}} + {2\; t_{H}}}$

where ρ_(s)=3.39×10⁻⁷ g cm⁻² is the sheet density of MoS₂, N is thenumber of the MoS₂ sheets, msurf=7.15×10⁻²² g is the mass of one SCmolecule, σ=1.35 nm⁻² is the surface packing density of SC on MoS₂,ρ_(H2O) is the density of water, t_(H)=3.3 nm is the assumed hydrationshell thickness, t_(MoS2)=0.67 nm is the MoS₂ interlayer distance, andt_(A)=0.355 nm is the assumed anhydrous shell thickness. The values forσ, t_(H), and t_(A) are based on previously established values forSC-encapsulated graphene. The resulting buoyant densities are presentedin FIG. 7C, where SC-encapsulated MoS₂, even in the monolayer limit, ispredicted to be more dense than iodixanol, the density gradient medium,at its solubility limit (1.32 g cm⁻³). Evidently, the relatively largesheet density of MoS₂ compared to graphene implies that the hydration ofSC is insufficient to lower the buoyant density of suspended MoS₂nanosheets to a level compatible with isopycnic DGU.

To overcome this issue, an alternative dispersant was considered forMoS₂ that would enable greater hydration and thus lower buoyant densityin aqueous solution. With reference to paragraph [0046], a nonionic,biocompatible, amphiphilic Pluronic® block copolymer was selected due toits relatively large molecular weight and long hydrophilic chains foreffective steric hindrance. Representative of numerous such commerciallyavailable Pluronic® copolymers, Pluronic F68 was employed. Inparticular, F68 is composed of a central hydrophobic polypropylene oxide(PPO) unit surrounding by hydrophilic polyethylene oxide (PEO) chains(FIG. 7A). To estimate the buoyant density of F68-encapsulated MoS₂, theparameters in the aforementioned model are modified as following:m_(surf)=1.40×10⁻²⁰ g is the mass of one F68 molecule, t_(A)=1.6 nm,t_(H)=20.6 nm, and σ is varied between 0.058 nm⁻² and 0.575 nm⁻² toaccount for the two likely extremes where the surface coverage of PPOchains on the MoS₂ surface ranges from 10% to 100%. This model suggeststhat the buoyant density of F68-MoS₂ is substantially reduced comparedto SC—MoS₂ and likely to fall within the achievable range ofiodixanol-based density gradients, especially in the limit of ultrathinMoS₂ (FIG. 7C).

To assess the effectiveness of F68-MoS₂ for DGU, 1 g of MoS₂ powder wasfirst exfoliated and dispersed in 2% weight per volume (w v⁻¹) aqueoussolution of F68 via tip ultrasonication. After ultrasonication, it wasfound that 17.1% of the initial MoS₂ mass was dispersed, as determinedby measuring the mass of the undispersed residual MoS₂ slurry. Theresulting F68-MoS₂ dispersion was placed in a step density gradient andultracentrifuged at 32 krpm for 24 hours to remove thick MoS₂ flakes andenhance the population of thin MoS₂ nanosheets (FIG. 8A). After thisconcentration step, 0.027 mg of MoS₂ flakes with thickness below 5 nmremain, of which 24% are single-layer MoS₂ flakes as determined by AFM.This level of exfoliation is comparable to previous literature results,and may be improved with the development of emerging techniques such asshear mixing or ball milling. After ultracentrifugation, dense iodixanolsolution containing 2% w v⁻¹ F68 was injected above the sedimentedaggregates at the bottom of ultracentrifuge tube to separate and allowfractionation of the concentrated MoS₂ nanosheets. The extractedF68-MoS₂ dispersion was stable for several months. It was observed thatwhen concentrated MoS₂ nanosheets were prepared using SC as thesurfactant, there was no isolation of a SC—MoS₂ band, which furtherillustrates the effectiveness of F68 as a dispersant for MoS₂.

After the concentration step, the fractionated F68-MoS₂ solution wasplaced at the bottom of a linear density gradient and ultracentrifugedat 28 krpm for 12 hours. The first iteration of DGU induces the F68-MoS₂nanosheets to separate into multiple visible bands throughout theultracentrifuge tube (FIG. 8B). These bands were recovered in 1 mm stepsusing a piston gradient fractionator and labeled with their position(i.e., fractions were recovered starting from 6 mm above the first bandand thus f7 indicates the fraction that encompasses the first band). Forfurther refinement, three fractions from the most well-defined bands(f7, f17, and f27) and relatively wider bands (f9, f13, and f23) wereextracted, and then placed at the top of a linear density gradient. Thesecond iteration of DGU was performed at 41 krpm for 12 hours, leadingto the formation of well-defined MoS₂ bands at their correspondingisopycnic points (dashed regions in FIG. 8C), which were thenfractionated for characterization. The topmost band, which will later beshown to be highly enriched in single-layer MoS₂, possesses a mass of0.002 mg, which implies that DGU captures 30.8% of the exfoliatedsingle-layer MoS₂ flakes (See, below, for more details on thecalculation of the DGU yield). It should be noted that similar DGUresults were achieved for other TMDs (e.g., DGU of WS₂, MoSe₂, and WSe₂,etc.), thus demonstrating the generality of the copolymer-assisted DGUfor thickness sorting of two-dimensional nanomaterials.

High angle annular dark field scanning transmission electron microscopy(HAADF-STEM) was used to verify the 2H structural phase and characterizeatomic-level defects of the MoS₂ nanosheets. FIG. 9A shows a schematicillustration of the 2H structural phase with trigonal prismaticcoordination. A Fast Fourier Transform from the HAADF-STEM image withtwo direction index is shown in FIG. 9B. FIGS. 9C and 9D show highresolution HAADF-STEM images of MoS₂ nanosheets before and after DGU.The inset in FIG. 9D shows the magnified STEM image with the position ofMo (blue) and S (brown) atoms. These STEM images reveal that thepristine 2H semiconducting structure of MoS₂ is preserved with minimalsurface or edge defects following DGU processing.

Atomic force microscopy (AFM) was used to characterize the thickness andsize of the sorted MoS₂ nanosheets. AFM images (FIG. 10A) indicate thatthe most buoyant fraction (f7) contains predominantly monolayers, whilethe less buoyant fraction (f17) primarily consists of MoS₂ multilayers.From the line profile, a monolayer MoS₂ flake in f7 has ˜1 nm thickness.This measured thickness is slightly larger than previously reportedvalues, which is reasonable due to the presence of residual F68. FIGS.10B and 10C show the AFM-measured thickness and area histograms for MoS₂nanosheets from the f7, f17, and f27 fractions. These histograms wereobtained from greater than 100 individual MoS₂ flakes from eachfraction. The average flake thicknesses for fractions f7, f17, and f27are 1.02, 1.84, and 2.52 nm, respectively, thus demonstrating effectivethickness sorting by DGU. In contrast, the flake area histograms showsignificant overlap, which is consistent with the buoyant density oftwo-dimensional nanomaterials being independent of lateral area.Overall, it is evident that the MoS₂ DGU separation is driven bythickness instead of the lateral size with ˜86% of the MoS₂ nanosheetsfrom f7 having a thickness less than 1.2 nm, which corresponds to singlelayers of MoS₂.

Based on the measured thickness and buoyant density values, the MoS₂experimental data are plotted with the geometrical buoyant density modelin FIG. 11A. The experimental values imply a Pluronic F68 packingdensity σ of 0.244 nm⁻². Since the PPO chain of Pluronic F68 occupies anarea of approximately 1.74 nm² on the MoS₂ surface, this packing densitycorresponds to ˜42.5% surface coverage of Pluronic F68. The surfacecoverage of F68 for WS₂, MoSe₂, and WSe₂ are determined to be 61.4%,68.2% and 57.0%, respectively. These experimentally determined surfacecoverage correlate with the relative hydrophobicity of each TMD. Inparticular, the most hydrophilic MoS₂ surface shows the lowest F68surface coverage, which is consistent with expectations since F68interacts with the TMD surface via its hydrophobic PPO chains.

Following DGU, optical absorbance spectra for fractions f7, f17, and f27in addition to the MoS₂ dispersion before separation were measured (FIG.11B). The direct MoS₂ excitonic transition peaks at ˜610 and ˜660 nm arepresent in all of the samples after DGU, further confirming that theoriginal 2H—MoS₂ crystal structure was maintained through the separationprocess. The two absorption peaks between 600 and 700 nm are attributedto the excitonic peaks of MoS₂. The weaker optical intensity of thesepeaks from f7, f17, and f27 are due to the relatively smallconcentration of MoS₂ in the solution following DGU. In addition, theblue shift observed in these peaks is consistent with the smallerlateral flake size following DGU, and the strong absorption below 400 nmis attributed to the density gradient medium (i.e., iodixanol).

Each MoS₂ fraction was also characterized by Raman spectroscopy (FIG.11C). In this case, MoS₂ films were prepared by vacuum filtration andtransferred onto a SiO₂ substrate at which point Raman spectra wereobtained using a beam size of ˜1 μm and an excitation wavelength of 514nm. The Raman spectra from the unsorted MoS₂ sample and fraction f27show two peaks, specifically the in-plane E¹ _(2g) mode at ˜382 cm⁻¹ andthe out-of-plane A_(1g) mode at ˜407 cm⁻¹, which are comparable to thoseof bulk MoS₂. As the number of layers decreases, the E¹ _(2g) mode isstiffened and the A_(1g) mode is softened, such that the peaks fromfraction f7 are shifted to ˜384 cm⁻¹ and ˜404 cm⁻¹, respectively.Additionally, the width of these two peaks is reduced in the morebuoyant fractions, which confirms that the flake thickness homogeneityis improved by DGU.

To further verify the isolation of MoS₂ monolayers, photoluminescencespectroscopy was performed on fraction f7 using an excitation wavelengthof 514 nm (FIG. 11D). For comparison, a photoluminescence spectrum wasobtained under identical measurement conditions from a micromechanicallyexfoliated monolayer of MoS₂, and both spectra were normalized usingtheir Raman spectra. The photoluminescence spectra from each fractionshow two peaks with comparable intensities at ˜610 and ˜660 nm that arewell correlated with the MoS₂ excitonic transitions. WS₂ nanosheets weresimilarly characterized following DGU, where photoluminescence was alsoobserved from the most buoyant fractions.

As demonstrated, isopycnic DGU enables solution-phase preparation ofcontrolled thickness TMDs. Specifically, the amphiphilic block copolymerPluronic F68 increases the hydration and thus reduces the effectivebuoyant density of TMDs into the range of standard density gradientmedia. Thickness sorting of TMDs is confirmed with AFM and Ramanspectroscopy, resulting in the emergence of photoluminescence from themost buoyant single-layered nanosheets. Furthermore, atomic-resolutionSTEM imaging verifies that the resulting thickness-sorted TMDs possesshigh crystal quality with low surface and edge defect density. Since DGUhas proven industrial scalability, this approach holds promise for thesolution-phase production of monolayered TMDs in emerging large-volumeapplications including photovoltaics, catalysis, biotechnology, andelectronics.

The present teachings also encompass articles of manufacture such asvarious electronic devices, optical devices, and optoelectronic devicesthat incorporate one or more transparent and electrically conductivecomponents. Instead of using existing transparent and electricallyconductive materials such as indium tin oxide, graphene films accordingto the present teachings can be used as transparent conductors. Forexample, sensors for detecting chemical or biological species can befabricated where the graphene film forms one of the conducting channels.Solar cells, light emitting diodes, and plasma and liquid crystaldisplays also can be fabricated based on graphene films according to thepresent teachings. The present graphene films can confer new advantagesto the devices described above such as mechanical flexibility and/orlonger lifetime.

EXAMPLES OF THE INVENTION

The following examples are provided to illustrate further and tofacilitate the understanding of the present teachings and are not in anyway intended to limit the invention.

Example 1 Solution Phase Preparation of Graphene

Graphene nanomaterial dispersions were prepared by horn ultrasonicationof naturally occurring graphite flakes in an aqueous solution containinga surface active component. More specifically, six grams of naturalgraphite flakes (3061 grade material from Asbury Graphite Mills, Asbury,N.J., USA) were added to 70 mL of a 2% w/v sodium cholate (SC) aqueoussolution inside a ˜120 mL stainless steel beaker. This mixture waschilled in an ice water bath and ultrasonicated using a FisherScientific Model 500 Sonic Dismembrator with a 13-mm-diameter tip forone hour at a power level of 51-52 W. Large initial loadings of graphitewere chosen to maximize the concentrations of graphene exfoliated intothe SC solution given the low cost of graphite flakes (˜$0.02 per gram).The sonicated graphene nanomaterial dispersions appeared as a gray-blackslurry, suggesting the presence of both thin graphene nanosheets andthicker graphite flakes.

Example 2 Sedimentation Centrifugation

Sedimentation centrifugation was performed to remove the fastsedimenting thick graphite materials from the sonicated graphenenanomaterial dispersions from Example 1. Specifically, the graphenenanomaterial dispersions were centrifuged in filled 2 mL eppendorf tubesusing a tabletop centrifuge (Eppendorf Model 5424 Microcentrifuge) usingfour different conditions summarized in Table 1. The black supernatantresulting from the sedimentation centrifugation processing was believedto consist of predominantly few-layer graphene nanoflakes. Thesedimented graphene nanomaterial dispersions were observed to be stablefor several weeks at loadings in excess of 90 μg/mL. Aftercentrifugation, the top 1 mL layer of the dispersion was decantedcarefully from each eppendorf tube. Optical absorbance measurements weretaken with a Cary 500 spectrophotometer (Varian) to estimate theconcentration of graphene nanomaterials in the dispersions using anaverage absorption coefficient for graphene of 2,460 mL⁻¹ m⁻¹ at awavelength of 660 nm. Contributions from the optical cuvette and sodiumcholate solution were subtracted from the spectra of the graphenedispersions. Table 1 lists the concentration of graphene nanomaterialsin the sedimented dispersions as determined from the absorbancemeasurements.

TABLE 1 Sedimentation Processing Parameters CentrifugationCentrifugation Relative Graphene Concentration Time (min) Speed (rpm)(speed)²(time) (mg mL⁻¹) 10 750 1 0.25 5 5000 22.2 0.23 5 15000 200 0.2060 15000 2400 0.09

Example 3 Concentration of Graphene Dispersions by Ultracentrifugationin a Step Gradient

To obtain concentrated dispersions of graphene nanoflakes, thesedimented dispersions from Example 2 were centrifuged in a step densitygradient. Specifically, the step gradients were prepared from a dense 6mL underlayer containing about 60% w/v iodixanol (density of about 1.32g mL⁻¹) and about 2% w/v SC, followed by a graphene overlayer of ˜32 mL(density of about 1.0 g mL⁻¹) added carefully on top, andultracentrifuged in an SW 28 rotor (Beckman Coulter) for 24 hours at 28krpm and a temperature of 22° C. Ultracentrifugation of the stepgradients caused the graphene nanosheets to sediment rapidly to thepoint where the density of the medium changed discontinuously. In thisregion, the few-layer graphene nanoflakes with low buoyant densitieshalted their sedimentation as they reached their isopycnic points whilethe denser thick graphite flakes continued their motion until theyeventually form a pellet at the bottom of the centrifuge tube. This stepgradient approach thereby eliminated a large portion of the thickcomponents in the dispersion without removing valuable few-layernanomaterials that also could be eliminated by simple centrifugationwithout the use of a dense underlayer. Following ultracentrifugation, a60% w/v iodixanol, 2% w/v SC displacement layer was slowly infused nearthe band of concentrated graphene nanomaterials to both separate it fromthe dense material below and to raise the position of the band in thecentrifuge tube for more reliable fractionation. The concentratednanomaterials was then collected near the step in the gradient using apiston gradient fractionator (Biocomp Instruments) to provide a highlyconcentrated graphene nanomaterial dispersion.

Example 4 Separation of Few-Layer Graphene Materials by ThicknessesUsing Density Gradient Ultracentrifugation

To separate the few-layer graphene nanomaterials by their thicknesses,the concentrated graphene nanomaterial dispersion collected from Example3 was subjected to two iterations of density gradientultracentrifugation (DGU). The relevant DGU conditions used for thefirst and second iteration separations are summarized in Table 2. Thefirst iteration used the maximum volume of concentrated graphenenanomaterial dispersion that could be added to a 4 mL solution with adensity of 46% w/v iodixanol. For the second DGU iteration, the graphenenanomaterial dispersions were diluted to 9-16% w/v iodixanol to decreaseviscosity, increase the graphene sedimentation rate, and enable layeringon the top of the density gradient.

More specifically, in the first iteration, the concentrated graphenedispersion was injected at the bottom of the linear density gradient andcentrifuged for 24 hours at a maximum centripetal acceleration of141,000 g. During this process, the graphene nanosheets moved upwards inthe centrifuge tube to their isopycnic points. FIG. 1C is a photographof the centrifuge tube following the separation. Multiple gray bands atdifferent locations inside the gradient were observed. These bands wererecovered in 1 mm steps using a piston gradient fractionator. Of theresulting 32 fractions, five were selected for a second iteration ofDGU: fractions f4, f10, and f22, which corresponded to the thinnestbands observed; and fractions f16 and f28, which were part of broaderbands. To achieve further density gradient refinement, the graphenenanomaterial dispersion was loaded at the top of a second densitygradient forcing the graphene flakes to move downward in the centrifugetube to their respective isopycnic points. This second DGU iterationremoved slow moving, low buoyant density materials that did not reachtheir isopycnic points in the first iteration.

TABLE 2 conditions used for DGU Separations First DGU Iteration SecondDGU Iteration Overlayer ~13 mL, 0% w/v iodixanol 0 to 2 mL, 0% w/viodixanol Graphene 4 mL, 46% w/v iodixanol, 3 to 5.5 mL, between 9 Layerconcentrated graphene to 16% w/v iodixanol dispersion (homogeneousdensity) Linear Density 15 mL, 25% to 45% w/v 5 mL, 30% to 50% w/vGradient iodixanol iodixanol Underlayer 6 mL, 60% w/v iodixanol 1.5 mL,60% w/v iodixanol Rotor SW 28 SW 4l Ti Centrifugation 28 krpm for 24hours 41 krpm for 12 hours at 22° C. Parameters at 22° C.

Example 5 Assessment of Thicknesses of Graphene Nanomaterials by AtomicForce Microscopy and Raman Spectroscopy Example 5.1 Sample Preparation

The DGU-processed graphene nanomaterials were characterized by bothatomic force microscopy (AFM) and Raman spectroscopy. Samples wereprepared by depositing graphene nanoflakes onto Si wafers capped by a100-nm thick oxide. Prior to deposition, the wafers were immersed in an2.5 mM (3-aminopropyl)triethoxysilane aqueous solution to functionalizethem with a self-assembled monolayer, dried with a stream of N₂, rinsedwith water, and then dried again. The graphene nanomaterial dispersionwas typically diluted by a factor of five with a 2% w/v sodium dodecylsulfate aqueous solution to improve the yield of the deposition. A dropof this diluted solution was then applied to the receiving wafer andleft for 10 minutes. The drop was blown off the wafer with a stream ofN₂, followed by rinsing the wafer in water for ˜15 seconds, and dryingby nitrogen. To remove residual surfactants and iodixanol, the graphenesamples were annealed in air for one hour at about 250° C. For betterAFM imaging, graphene samples that had undergone density processing weresometimes dialyzed to remove iodixanol. For ˜2 mL of graphenedispersion, dialysis was typically done with 20,000 molecular weightcut-off dialysis cassettes (Pierce Slide-A-Lyzer) using a 1.75 L, 2% w/vSC aqueous bath for ˜48 hours.

Example 5.2 Atomic Force Microscopy

AFM images were obtained using a Thermo Microscopes AutoprobeCP-Research AFM operating in tapping mode with conical probes(MikroMasch, NSC36/Cr—Au BS). All AFM images used for thicknessmeasurements were generated using one of two AFM probes. To ensure thetwo probes produced the same thickness values, multiple graphene flakesfrom fraction f4 were imaged by both probes and compared. In addition,highly-oriented pyrolytic graphite (HOPG) was imaged as a calibrationstandard for accurate height measurements. All images in the analysiswere 2 μm×2 μm and collected under identical scan parameters. Graphenesheets that were part of bundles were excluded from the analysis. Inaddition, sub-2500 nm² area flakes were neglected due to the uncertaintyin their thickness measurements as were residual SC or iodixanol whosethickness exceeded 5 nm.

Graphene flakes from fraction f4 exhibit an average thickness of about1.1 nm. Single-layer graphene on SiO₂ typically has an apparentthickness of ˜1 nm as a result of adsorbed water (see Novoselov et al.,Science, 306(5696): 666-669 (2004)). The slightly increased thickness ofthe materials from fraction f4 could be due to residual sodium cholatemolecules on the graphene surface. In contrast, the graphene sheets fromf16 were found to have an average thickness of 1.5 nm.

FIGS. 2A and 2B present the thickness histograms of several sortedgraphene fractions (Example 4) as well as the concentrated (Example 3)and sedimented (Example 2) graphene dispersions. These histograms werecalculated from at least 100 individual flakes using multiple 2 μm×2 μmAFM images with the average thickness measured over the area of eachflake. Comparison of the thickness distributions of the sedimented,concentrated, and f4 graphene solutions in FIG. 2A shows progressivesharpening of the distributions with increasing buoyant densityrefinement.

With continued reference to FIG. 2A, it can be seen that for thesedimented graphene solution, 37% of the flakes was found to havethicknesses greater than 2 nm. By comparison, following concentrationstep gradient processing, only 2.6% of the dispersion was found to havethicknesses greater than 2 nm. Furthermore, it can be seen thatfollowing DGU, flakes having thicknesses greater than 2 nm essentiallyare absent in fraction f4. Instead, at least about 80% of the grapheneflakes from fraction f4 were found to have thicknesses of 1.2 nm orless, suggesting that most of these graphene flakes likely correspond tosingle-layer graphene. In contrast, only 24% of the concentratedgraphene consisted of single-layer material.

Referring to FIG. 2B, the thickness distributions of the graphene sortedusing DGU show a monotonic increase in the average flake thickness withincreasing buoyant density. Comparing the mean flake thickness of thegraphene materials in fractions f4, f16, and f28 to the sedimented orconcentrated dispersion shown in FIG. 2A, it can be seen clearly thatthe present methods allow separation of two-dimensional nanomaterials bytheir thicknesses.

Example 5.3 Geometrical Model for Determining Buoyant Density ofFew-Layer Graphene Flakes

Without wishing to be bound by any particular theory, it is believedthat upon contact with the appropriate surface active component(s)according to the present teachings, the graphene materials can bedispersed as individual encapsulated flakes, thus providing a graphenedispersion that can remain stable for an extended period of time. Togain further insight into the ordering of surface active components suchas sodium cholate on the graphene surface, the inventors developed ageometrical model of the buoyant density of the graphene-SC complex. Inthis model, and as schematically illustrated in FIG. 3A, the thicknessof the graphene sheet is defined by N, which specifies the averagenumber of graphene layers inside the sheet separated by the grapheneinterlayer distance t_(gr)=0.34 nm. On both sides of the graphene sheetis an anhydrous layer of thickness t_(A) containing the SC encapsulationlayer. The SC molecules in this region coat the graphene surface withsurface packing density a. Surrounding this SC layer is anelectrostatically bound hydration shell of thickness t_(H). Thishydration layer has the lowest density of any of the components in thecomplex and hence serves to decrease the buoyant density of thegraphene-SC assembly. The resulting buoyant density ρ(N) is then:

${\rho (N)} = \frac{{\rho_{S}N} + {2\; m_{surf}\sigma} + {2\; \rho_{H_{2}O}t_{H}}}{{\left( {N + 1} \right)t_{gr}} + {2\; t_{A}} + {2\; t_{H}}}$

where ρ_(S)=7.66×10⁻⁸ g cm⁻² is the sheet density of graphene,m_(SC)=7.15×10⁻²² g is the mass of one SC molecule, and ρ_(H) ₂ _(O) isthe density of water.

The graphene buoyant density model was applied to the experimental databy assuming the anhydrous shell thickness t_(A) was 0.355 nm (see Arnoldet al., ACS Nano., 2(11): 2291-2300 (2008)). Furthermore, the apparentthickness for single-layer graphene was taken to be the averagethickness of 1.1 nm measured for graphene sheets from fraction f4. N forsubsequent fractions was then calculated from their average meanthicknesses and the graphite interlayer spacing. With these conditionsin place, the model yields a SC surface packing density σ of 1.35 nm⁻²and a hydration layer thickness t_(H) of 3.3 nm. Because SC occupiesapproximately a ˜0.7 nm² area on the graphene surface (see Arnold etal., ACS Nano., 2(11): 2291-2300 (2008)), this surface densitycorresponds to ˜94% surface coverage of SC (schematically illustrated inFIG. 1B). The small area of graphene occupied by each SC molecule alsoimplies that it is possible for the SC encapsulation layer toaccommodate variations in graphene thickness on length scales of severalnanometers. Consequently, without wishing to be bound by any particulartheory, it is believed that a continuum of mean graphene flakethicknesses can be separated using DGU depending on how the flakes areexfoliated (FIG. 3B).

Example 5.4 Raman Spectroscopy

Raman spectroscopy of graphene flakes on SiO₂ was performed using aRenishaw in Via Raman Microscope at an excitation wavelength of 514 nm.To obtain a random sampling of the graphene at multiple locations,spectra were measured at multiple positions spaced at least 5 μm apart.Spectra were obtained using a beam size of 1-2 μm on samples with a highsurface coverage of graphene enabling multiple flakes to be probed in asingle measurement. For these map scans, 2D, G, and D bands weremeasured consecutively to ensure the relative intensities of the peakswere not affected by drift of the translation stage.

Typical Raman spectra from the sorted graphene samples display four mainpeaks: the G band at ˜1590 cm⁻¹, the 2D (or G′) band at ˜2700 cm⁻¹, andthe disorder-related D and D′ peaks at ˜1350 cm⁻¹ and ˜1620 cm⁻¹,respectively (FIGS. 4A and 4B). The Raman spectra show systematicchanges in the G and 2D peaks as a function of the thicknessdistribution of the graphene flakes. For example, it can be observedthat the 2D peak decreases in intensity and broadens with increasingmean flake thickness. To gather sufficient statistics for thesevariations, spectra were collected from at least 30 different locationsand mean and standard deviation information was extracted from thesedata. FIG. 4C presents the I(2D)/I(G) ratio and full-width at halfmaximum (FWHM) of the 2D band as a function of the average thickness ofthe sorted and concentrated graphene dispersions.

It was observed that as the thickness of the graphene flakes increases,I(2D)/I(G) decreases monotonically from a high of 2.1±0.2 forsingle-layer graphene to 0.8±0.1 for quadruple-layer graphene. FWHM(2D),on the other hand, increases with graphene thickness nearly doublingbetween single- and quadruple-layer samples. Similar trends in bothI(2D)/I(G) and FWHM(2D) as a function of graphene layer number havepreviously been observed for CVD grown graphene samples (see Reina etal., Nano. Lett., 9(1): 30-35 (2009)), and should prove useful for morerapid screening of DGU-sorted graphene. Similar to CVD-graphene samplesand those grown on SiC (see Faugeras et al., Appl. Phys. Lett., 92(1):011914-3 (2008)), the 2D band of multilayer graphene appears to be bestdescribed by a single Lorentzian lineshape, as opposed to the fourcomponent lineshape observed for samples produced by micromechanicalcleavage (see Ferrari et al., Phys. Rev. Lett., 97: 187401 (2006)).Because these four components arise from the close interaction betweenABAB stacked graphene layers, their absence implies weak interlayercoupling and hence non-ABAB stacking. This source of disorder could becaused during horn ultrasonication or from rebundling of previouslyexfoliated graphene sheets. The disorder-related D peak is relativelyintense compared to the G band in these samples, most likely as a resultof defects within the graphene sheets or from the small size of theflakes, which should increase the number of disordered graphene edgesprobed in the measurement. The ratio of the intensities of the D and Gpeaks I(D)/I(G) remains fixed at ˜0.93 for both the sedimented anddensity-refined material, which indicates that ultracentrifugation didnot contribute additional defects to the graphene. This I(D)/I(G) valueis comparable to that observed in highly reduced graphene oxide (see Gaoet al. Nature Chem., doi:10.1038/nchem. 281 (2009)), and is less thanthat measured for lithographically patterned graphene nanoribbons (seeJiao et al., Nature, 458(7240): 877-880 (2009)).

Example 6 Graphene Transparent Conductors Example 6.1 Preparation ofTransparent Conductive Films

To assess the electrical properties of graphene material sorted by thepresent methods, graphene films were prepared using the method describedin Wu et al., Science, 305: 1273 (2004), by filtering approximately 2 mLof graphene dispersion in a 2% w/v SC aqueous solution under vacuumthrough mixed cellulose ester membranes (Millipore) having a 50 nmaverage pore size. After the dispersion had passed through the membrane,the film was left to set over 15 minutes. Residual surfactant andiodixanol were rinsed out of the film by filtering through ˜30 mL ofwater. To prevent the film from lifting off the membrane during thisstep, a protective layer of isopropyl alcohol was slowly added on top ofthe film followed by a slow but steady stream of the water rinse. Thefiltered films were then affixed to glass substrates by soaking them inethanol and pressing the graphene side firmly into the glass. The stillwet graphene film and membrane were promptly introduced to an acetonevapor bath that dissolved away the mixed cellulose ester membrane. Themembranes were further dissolved in three subsequent acetone liquidbaths and a final ethanol liquid bath.

Example 6.2 Effect of Annealing of Graphene Transparent Conductors

It was found that the sheet resistance of graphene transparentconductive films (Example 6.1) could be decreased by an average factorof 2-4 by annealing them in air. Specifically, film samples wereannealed for two hours at about 250° C., which was observed to have theeffects of increasing the film conductivity, while increasing thetransmittance by about 1%. Without wishing to be bound by any particulartheory, it is believed that annealing likely removed some of theiodixanol and sodium cholate remaining in the film and enabled thegraphene sheets to reorder to improve flake-flake contacts. The sheetresistance and transmittance of films produced from concentratedgraphene and the sorted fraction f4 before and after annealing are shownin FIG. 5A. It was observed that annealing provided greater improvementsin sheet resistance for films of higher transmittance. Without wishingto be bound by any particular theory, it is believed that films of hightransmittance are closer to the percolation threshold of graphene andare more sensitive to changes in flake network connectivity.

AFM images of the annealed films indicate the graphene flakes form adisordered network. Folded flakes can be discerned in the images alongwith rough areas that are most likely caused by residual surfactants,iodixanol, or the filter membrane. The films possess high opticaltransmittance from ˜300 nm to 3300 nm, revealing a wide transmittancewindow that is well suited for infrared applications.

Example 6.3 Transparent Conductors Produced from Sedimented Dispersions

To compare between the properties of transparent conductive filmsprepared from DGU processing and those prepared from sedimented graphenesolutions, transparent conductors from sedimented graphene dispersionswere prepared under different centrifugation conditions. FIG. 5Bpresents the sheet resistance and transmittance of films prepared fromthe graphene dispersions described in Table 1. The variation in theperformance of these films is relatively small compared to that observedfollowing density differentiation. This result indicates that any sizesorting effect is small for SC-encapsulated graphene produced by thistype of sedimentation centrifugation.

Four-point probe measurements of the film sheet resistance indicatedthat DGU processing yields significant improvements in the transparentconductive properties of the graphene films. Firstly, all films producedusing buoyant density sorting demonstrated improved conductivitycompared to films produced from sedimented graphene solutions (FIGS. 6Aand 6B). For the films produced from the concentrated, f16, and f28dispersions, this improvement is ˜45%. Secondly, the films producedusing predominantly single layer graphene flakes (f4) offer the besttransparent conductor performance. These highly refined materialsexhibit sheet resistances that are approximately half that of the otherdensity processed material. Analysis of the graphene flakes indicatesthat the f4 material has the largest mean area (16,000 nm²) of all thematerials used for transparent conductors. A large lateral area shouldresult in fewer graphene-graphene contacts required for charge transportacross the film and thus implies increased film conductivity. However,the differences in transparent conductor performance between theconcentrated and sedimented solutions suggest that the graphenethickness distribution also can play an important role in theconnectivity of the graphene network. The larger proportion of thickgraphene sheets in the sedimented solution may disrupt the ideal closepacked structure of the network, which would reduce the overlap betweenneighboring sheets. In contrast, the highly flexible single-layergraphene sheets deposited from solution are expected to coat underlyinglayers with greater conformity, resulting in improved graphene-graphenecontacts.

Example 7 Sorting of Non-Graphene Two-Dimensional Nanomaterials byThickness

Using methods of the present teachings, two-dimensional nanomaterials ofcontrolled thickness can be generated from crystalline materialsincluding, but not limited to, graphite, MoS₂, and hexagonal BN. MoS₂ isa semiconducting transition metal dichalcogenide consisting of layers ofmolybdenum coordinated with six sulfide ligands. Hexagonal BN is asemiconductor material with a structure analogous to that of graphite.

Step 1—Dispersion:

Base dispersions of the starting crystalline materials typically weregenerated by loading 10 mL of a 2% w/v SC (Sigma-Aldrich) aqueoussolution with one gram of bulk crystallite powder. The mixtures werethen subjected to horn ultrasonication at 160 W for one hour using aFisher Scientific Model 500 Sonic Dismembrator with a tapered microtipprobe. Poorly dispersed materials were removed by centrifugation at21,130 g relative centrifugal force for 5 minutes. The supernatant fromeach centrifuge tube was recovered to form the base dispersion. The basedispersion of MoS₂ was observed to have a yellow/orange color, whereasthe base dispersion of BN was iridescent and appeared slightly white.Atomic force microscopy (AFM) images of thin films deposited ontoSiO₂-capped Si wafers from base dispersions of graphite, MoS₂, andhexagonal BN prepared according to the procedures described aboveconfirm the presence of crystallites with thicknesses ranging from about1 nm to about 10 nm.

Step 2—Concentration in Step Gradient:

The base dispersions were then inserted into a step gradient andconcentrated. Step gradients were formed by first adding a ˜2.5 mL layerof solution of about 1.32 g/mL density consisting of ˜2% w/v sodiumcholate and ˜60% w/v iodixanol to the bottom of the centrifuge tube. A˜9.5 mL layer of the base dispersion was added on top of the underlayercompleting the step gradient. The layered centrifuge tubes wereultracentrifuged at 41 krpm in a SW41 Ti (Beckman Coulter) rotor for 14hours. The concentrated dispersions were recovered using a two-stepfractionation process. First, a displacement layer consisting of 2% w/vsodium cholate and 60% w/v iodixanol (OptiPrep; Sigma-Aldrich; 1.32 g/mLdensity) was slowly infused just below the band of concentratedmaterial. This solution, mixing relatively little with the surroundingliquid, migrated to the position in the step gradient that matched itsdensity and displaced upwards all crystallites with buoyant densitiesless than 1.32 g/mL. Following upward displacement, the thin band ofconcentrated two-dimensional nanomaterials was recovered using a pistongradient fractionator (Biocomp Instruments).

Step 3—Sorting in Density Gradient:

The crystallite dispersions were added to density gradients loaded with2% w/v sodium cholate throughout. To generate the density gradients, a1.5 mL underlayer consisting of 60% w/v iodixanol was added first to thebottom of the centrifuge tube and a 5 mL linear gradient with densityvarying from about 20% to about 45% w/v iodixanol was formed above. Thedispersion of crystallites with iodixanol content adjusted to about40.8% w/v was then slowly infused into the lower portion of the gradientto a volume of 0.88 mL. Then, the remaining volume of the centrifugetube was filled with 2% w/v sodium cholate aqueous solution to preventtube collapse under high centrifugal forces. The centrifuge tubes werespun at 41 krpm for 14 hours in a SW41 Ti (Beckman Coulter). Followingcentrifugation, the separated two-dimensional nanomaterials werecollected using a piston gradient fractionator.

Following ultracentrifugation of concentrated dispersions of graphite,MoS₂, and hexagonal BN, discrete bands of material were observed insidethe centrifuge tube for all three materials. For graphite crystallites,gray bands of spatially separated material were observed under multipledensity gradient conditions. For the MoS₂ crystallites, a singleisolated yellow band was detected following DGU with denser materialforming a broader yellow region nearer the bottom of the centrifugetube. For BN samples, crystallites were difficult to detect directly byeye since hexagonal BN is a large band gap semiconductor and hence istransparent in the visible portion of the electromagnetic spectrum.However, by recording the light scattered by the crystallites inside thecentrifuge tube, it was possible to observe a discrete band of buoyantmaterial isolated from a broad band of much higher density.

The formation of discrete bands of two-dimensional nanomaterialsfollowing DGU provides strong evidence for sorting by number of atomiclayers. The buoyant density of the crystallite-surfactant complex ismost strongly affected by the atomic structure of the two-dimensionalnanomaterial. Hence, the existence of crystallites with distinct buoyantdensities implies that these crystallites differ by characteristics thatvary discretely. As a result, and without wishing to be bound by anytheory, it is believed that the crystallites having different buoyantdensities consist of different numbers of atomic layers.

Example 8 Preparation of Graphene Nanoribbons

Graphene nanoribbons (GNRs) were obtained from highly oriented pyrolyticgraphite (HOPG) dispersed in sodium cholate solution. HOPG flakes wereinitially added to a 1% w/v sodium cholate aqueous solution at a 1 mg/mLloading and horn ultrasonicated for 3 hours at 200 W. The resultingdispersion was then concentrated in a step gradient as described inExamples 3 and 7 and fractionated using a piston gradient fractionationsystem without infusing a displacement layer. Subsequently, theconcentrated dispersion was incorporated into a density gradient similarto that described in Example 7 except with 1) a linear gradient varyingfrom 20% to 50% w/v iodixanol, 2) an initial graphene layer density of45% w/v iodixanol, and 3) a loading of 1% w/v sodium cholate throughoutthe gradient. The layered centrifuge tube was then ultracentrifuged in aSW41 Ti rotor at 41 krpm for 20 hours. Following centrifugation, theseparated GNRs were collected using a piston gradient fractionator.

AFM analysis of the separated GNRs reveal that the GNRs have widthsbelow about 10 nm and lengths up to about 1 μm. Typical thicknessesrange from about 0.8 nm to about 1.8 nm.

Example 9 Dispersion of Graphene Using Various Surface Active Components

Graphene suspensions were prepared in a variety of surface activecomponents to determine their efficiency at stably encapsulatinggraphene in aqueous solutions. All graphene dispersions listed belowwere prepared in an identical manner. Natural graphite flakes (3061grade material from Asbury Graphite Mills) weighing 600 mg±5 mg wereadded to 8 mL of an aqueous solution containing a loading of the surfaceactive component of 1% weight per volume. The mixture was hornultrasonicated (Fisher Scientific Model 500 Sonic Dismembrator equippedwith a 3-mm-diameter tip) at a power level of 16-18 W for 30 minutes ina cooling bath of water. Following ultrasonication, thegraphite/graphene slurry was centrifuged (Eppendorf Model 5424Microcentrifuge) in 1.5 mL plastic tubes for 5 minutes at 15 krpm(21,130×g). The top 1 mL of solution containing few-layer graphenenanomaterials was carefully decanted. The concentration of graphene ineach of the suspensions was determined using optical absorptionmeasurements. An extinction coefficient of 2460 mL⁻¹ cm⁻¹ at awavelength of 660 nm previously reported for graphene was used for allmeasurements (see Y. Hernandez et al, Nature Nanotech. 3, 563 (2009)).

TABLE 3 Graphene Dispersion Efficiency of Bile Salt Surfactants BileSale Graphene Concentration (mg/mL) Sodium cholate 0.54 Sodiumdeoxycholate 0.34 Sodium taurodeoxycholate 0.29

TABLE 4 Graphene Dispersion Efficiency of Anionic Surfactants AnionicSurfactant Graphene Concentration (mg/mL) Sodium decyl sulfate 0.11Sodium undecyl sulfate 0.14 Sodium dodecyl sulfate 0.16 Lithium dodecylsulfate 0.15 Sodium dodecylbenzenesulfonic acid 0.33

TABLE 5 Graphene Dispersion Efficiency of Cationic Surfactants GrapheneConcentration Cationic Surfactant (mg/mL) Dodecyltrimethylammoniumbromide 0.16 Myristyltrimethylammonium bromide 0.19Hexadecyltrimethylammonium bromide 0.25 Hexadecyltrimethylammoniumchloride 0.15 Hexadecyltrimethylammonium hydrogen sulfate 0.12

TABLE 6 Graphene Dispersion Efficiency of Polymeric Surfactants PolymerGraphene Concentration (mg/mL) Sodium carboxymethylcellulose 0.55Tween ® 20 0.08 Tween ® 85 0.03

TABLE 7 Graphene Dispersion Efficiency of Polyvinylpyrrolidone MolecularWeight (kDa) Graphene Concentration (mg/mL) 10 0.25 29 0.32 55 0.30 3600.31 1300 0.28

TABLE 8 Graphene Dispersion Efficiency of Pluronic ® Block CopolymersPluronic ® Molecular PEO PPO Graphene Block Weight Molecular MolecularConcentration Copolymer (Da) Weight (Da) Weight (Da) (mg/mL) F108 1460011680 2920 0.13 F127 12600 8820 3780 0.18 F38  4700 3760 940 0.17 F68 8400 6720 1680 0.20 F77  6600 4620 1980 0.27 F87  7700 5390 2310 0.19F88  11400 9120 2280 0.18 F98  13000 10400 2600 0.18 P103 4950 1485 34650.07 P104 5900 2360 3540 0.12 P123 5750 1725 4025 0.06 P84  4200 16802520 0.12

TABLE 9 Graphene Dispersion Efficiency of Tetronic ® Block CopolymersTetronic ® Molecular PEO PPO Graphene Block Weight Molecular MolecularConcentration Copolymer (Da) Weight (Da) Weight (Da) (mg/mL) 304 1650660 990 0.18 904 6700 2680 4020 0.10 908 25000 20000 5000 0.19 110715000 10500 4500 0.24 1307 18000 12600 5400 0.23

Example 10.1 Dispersion and Density Gradient Ultracentrifugation

1 g of MoS₂ powder (American Elements) was dispersed in 70 mL of 2% wv⁻¹ Pluronic F68 (BASF) aqueous solution via ultrasonication using a0.125 inch tip in a steel beaker at 25 W for 2 hours. Then, 32 mL ofdispersion was carefully added on top of a 6 mL underlayer of 60% w v⁻¹iodixanol and ultracentrifuged at 32 krpm for 24 hours at 22° C. using aSW32 Ti rotor (Beckman-Coulter). Following ultracentrifugation, 3 mL of60% w v⁻¹ iodixanol was injected to separate ˜10 mL of concentrated MoS₂nanosheet solution, which was then fractionated using a piston gradientfractionator (BioComp Instruments). For the first iteration, theconcentrated MoS₂ solution was diluted to contain 46% w v⁻¹ iodixanol,and placed under a linear density gradient of 25% to 45% w v⁻¹iodixanol. The linear density gradient was then ultracentrifuged at 28krpm for 12 hours at 22° C. Following the first iteration, each fractionwas diluted to contain 9% w v⁻¹ iodixanol and placed on top of a lineardensity gradient of 30% to 50% w v⁻¹ iodixanol for the second iteration.The linear density gradient was then ultracentrifuged in an SW41 Tirotor (Beckman-Coulter) at 41 krpm for 12 hours. All density gradientand injection solutions contained 2% w v⁻¹ F68. (See, Table 10.)

TABLE 10 DGU Conditions for the First and Second Iterations. 1^(st)Iteration 2^(nd) Iteration Density Volume Density Volume DGU Condition(w/v) (mL) (w/v) (mL) Overlayer  0% ~15 0% 2 Linear Density 25%-45% 1630%-50% 5 Gradient MoS₂ Layer 46% 3.5 9% 3-5 Underlayer 60% 6 60%   1.5Ultracentrifugation 28k rpm for 12 41k rpm 12 Condition hours at 22° C.hours at 22° C.

Example 10.2 Thickness Sorting of Other TMD Nanosheets

Identical conditions were used for thickness sorting of pristine WS₂,MoSe₂, and WSe₂.

Example 11.1 Sample Preparation for Scanning Transmission ElectronMicroscopy

MoS₂ dispersions from each step (after sonication before DGU and afterDGU) were collected and placed in 20 k MWCO dialysis cassettes (ThermoScientific) and dialyzed in 750 mL of 2% w v⁻¹ F68 aqueous bath for 24hours to remove the density gradient medium. To remove the surfactant,MoS₂ dispersions were mixed with isopropyl alcohol for 24 hours,filtered through mixed cellulose ester membranes (Millipore, 50 nm poresize), and rinsed with deionized water. The resulting aggregated MoS₂nanosheets were then bath sonicated (Branson ultrasonic cleaner 3510) toredisperse in deionized water.

Example 11.2 Measurement and Analysis

A drop of an aggregated solution of MoS₂ was deposited on a holey carbongrid. Scanning transmission electron microscopy (STEM) imaging wasperformed using an aberration-corrected JEOL ARM-200F microscopeequipped with a CEOS Cs probe-corrector on the illumination system. Theimages were collected using the high angle annular dark field (HHADF)detector. The probe size used for acquiring the HAADF-STEM images was 9C (˜23.2 pA). The collection angle used with a camera length of 8 cmranges from 50 to 180 mrad. The lens aberrations were optimized byevaluating the STEM tableau using a standard gold nanoparticle sample.The accelerating voltage was set to 200 kV, and no beam-induced damageoccurred during the observation of the sample. The images were collectedusing a dwell time of 31 μs; subsequently a maximum entropydeconvolution algorithm was applied to the images (DeConvHAADF iscommercially available from HREM Research Inc.).

Example 12.1 Sample Preparation for Atomic Force Microscopy

The separated MoS₂ fractions were dialyzed in 750 mL of 2% w v⁻¹ SC bathfor 48 hours to enable surfactant exchange. Prior to deposition, a SiO₂substrate was rinsed with acetone, methanol, and deionized water andimmersed in 2% Polyethylenimine (PEI) for 2 minutes to form aself-assembled monolayer. The substrate was then dried under nitrogengas, rinsed in deionized water, and dried again. The samples were dropcasted onto PEI-treated SiO₂ substrate for 5 minutes, dried undernitrogen gas, rinsed in deionized water, dried again, and annealed at250° C. for 1 hour to remove residual surfactants and iodixanol. Toincrease the areal density of MoS₂ flakes, this process was repeated 5to 10 times.

Example 12.2 Flake Thickness Measurement and Analysis

AFM images were obtained using a Cypher S AFM in tapping mode. Allimages were 2 μm by 2 μm with identical scan conditions (NCHR AFM tipswere used). An AFM image and line profile of the fraction f27 is shownin FIG. 13.

Example 13.1 Sample Preparation for Raman and PhotoluminescenceSpectroscopy

MoS₂ films were prepared via the vacuum filtration method. Inparticular, 2 mL of MoS₂ dispersion was filtered. The residualsurfactant and iodixanol were then removed by rinsing with 30 mL ofdeionized water. The resulting film was immersed in ethanol and pressedfirmly on to a SiO₂ substrate for 10 minutes by applying pressure with a1.5 kg weight. To remove the membrane, the substrate was suspended abovea boiling acetone bath at 85° C. at a 45° angle. After 15 minutes, thesubstrate was rinsed with ethanol, acetone, ethanol again, and deionizedwater, and then dried with nitrogen gas.

Example 13.2 Absorbance, Raman, and Photoluminescence Spectroscopy

Optical absorbance spectra were measured using a Cary 5000spectrophotometer (Agilent Technologies). The contribution from thecuvette and F68 was measured as a baseline and then subtracted from thespectra of the MoS₂ dispersions. Please note that the UV-Vis spectrawere measured over the wavelength range of 350 nm to 800 nm due to thestrong absorbance by iodixanol at wavelengths below 350 nm. The Ramanspectra and photoluminescence spectra of the MoS₂ nanosheets wereobtained using an Acton TriVista Confocal Raman System with anexcitation wavelength of 514 nm in multiple positions spaced at leastseveral microns apart. For the comparison of photoluminescenceintensity, micromechanically exfoliated monolayer MoS₂ was prepared viathe scotch tape method, and PL spectra were obtained under identicalmeasurement conditions (5× accumulation, 5000 ms exposure time, andidentical filters) by keeping the laser focusing height identical (thelaser is initially focused on the substrate, and then sample regions ofinterest are moved under the laser spot where Raman and PL spectra aresubsequently taken at the same location) for each sample (FIG. 14).

Example 14 Characterization of DGU-Sorted TMD Nanosheets

Following DGU, the collected fractions of WS₂ were characterized usingoptical absorbance, Raman, and photoluminescence spectroscopy. Prior tothe spectroscopic measurements, the measured buoyant densities of WS₂were compared to the buoyant density model of σ_(sc) and σ_(F68),leading to similar conclusions as MoS₂. The optical absorbance spectraof fractions f6 and f12 in addition to the concentrated andultrasonicated WS₂ dispersion before DGU were measured. The excitonictransition peak at ˜615 nm is observed in all samples. Each WS₂ fractionwas also characterized by Raman spectroscopy. In particular, a WS₂ filmwas prepared via vacuum filtration and transfer onto a SiO₂ substrate,and then Raman spectra were obtained using a beam size of ˜1 μm with anexcitation wavelength of 514 nm. The Raman spectrum from f12 has thein-plane 2LA mode at ˜355.5 cm⁻¹ and the out-of-plane A1g mode at ˜420.5cm⁻¹, which are comparable to those of bulk WS₂. In contrast, the Ramanspectrum from f6 shows a shift of ˜4 cm⁻¹ in the A_(1g) mode, which isconsistent with the previously reported result for thin WS₂ nanosheets.Photoluminescence spectra from each fraction were also obtained using anexcitation wavelength of 514 nm. The emission spectra from each fractionshow a peak at ˜615 nm that corresponds well to the absorption peak. Themost buoyant f6 fraction with an enriched population of WS₂ monolayersshows significantly enhanced photoluminescence intensity as compared tof12. The spectra were normalized by the concentration of WS₂, which wasdetermined from the optical absorbance spectra.

The buoyant density of MoSe₂ and WSe₂ fractions were measured and theaverage packing density of F68 on MoSe₂ and WSe₂ were calculated. Inaddition, each fraction was characterized using optical absorbance.

Example 15 Surface Coverage of Pluronic F68 on TMDs

As discussed above, before DGU, the following geometrical buoyantdensity model was used in order to assess the applicability of DGU toMoS₂ nanosheets:

$\begin{matrix}{{\rho (N)} = \frac{{\rho_{S}N} + {2\; m_{surf}\sigma} + {2\; \rho_{H_{2}O}t_{H}}}{{\left( {N + 1} \right)t_{{MoS}_{2}}} + {2\; t_{A}} + {2\; t_{H}}}} & (1)\end{matrix}$

where the packing density σ varies from 0.058 nm⁻² to 0.575 nm⁻² toaccount for the two extremes where the PPO chains cover the MoS₂ surfacefrom 10% to 100%, which corresponds to the gray area in FIG. 10A. Thehydration thickness t_(H) was fixed by the average shell thickness basedon the known micelle structure of Pluronic F68 using the followingequation:

$\begin{matrix}{t_{H\_ {avg}} = \frac{d_{F\; 68{\_ {avg}}} - d_{{PPO}\_ {Core}}}{2}} & (2)\end{matrix}$

where t_(H) _(—) _(avg) is the average hydration thickness, d_(F68) _(—)_(avg) is the average diameter of a Pluronic F68 micelle, and d_(ppo)_(—) _(core) is the average diameter of PPO core networks.

To assess the packing density and surface coverage of Pluronic F68 foreach TMD, the experimental values were determined from their measuredbuoyant densities:

$\begin{matrix}{\sigma_{TMD} = \frac{{\left\{ {{\left( {N + 1} \right)t_{TMD}} + {2\; t_{A}} + {2\; t_{H}}} \right\} {\rho (N)}} - {\rho_{s}N} - {2\; \rho_{H\; 2\; O}t_{H}}}{2\; m_{surf}}} & (3)\end{matrix}$

Using this model, the packing density and surface coverage of PluronicF68 on each TMD is shown in Table 11. From these results, it is clearthat the experimental packing density and surface coverage of F68 onTMDs are relatively lower than SC on graphene, likely due to the largermolecular weight and nonionic nature of Pluronic block copolymers. Thepacking density of Pluronic F68 on TMDs is correlated with thehydrophobicity of the TMDs, with the most hydrophilic MoS₂ showing thelowest surface coverage among the studied TMDs.

TABLE 11 Packing density and surface coverage of F68 on TMDs. Graphene -MoS₂ WS₂ MoSe₂ WSe₂ SC¹ Packing 0.244 nm⁻² 0.353 nm⁻² 0.392 nm⁻² 0.328nm⁻² 1.35 nm⁻² Density Surface 42.5% 61.4% 68.2% 57.0% 94% CoverageContact 60° 93° — 135-145° 85° Angle²⁻⁴ (500-650° C.)

Example 16 MoS₂ Flake Lateral Size Measurement and Analysis

Scanning electron microscopy (SEM) images were obtained using a HitachiSU 8030 FE-SEM. SEM images before and after DGU were obtained to comparethe average lateral size of MoS₂ flakes and a lateral size histogram wasobtained based on the images. According to the histogram, the averagelateral size of flakes was significantly reduced after DGU, which leadsto a blue shift in the optical absorption peaks of MoS₂ as observedpreviously. The lateral size histogram from the SEM images of f7 and f17was also obtained and found to agree well with the histogram from theAFM images.

Example 17 Single-Layer MoS₂ Separation Yield Via DGU

1 g/70 mL is the initial loading for the MoS₂-F68 dispersion. After twohours of tip sonication, 0.17 g of MoS₂ is suspended in solution, asdetermined by mass measurement of the residual MoS₂ slurry. Theconcentration step is then performed to remove all flakes greater than 5nm in thickness and concentrate the remaining thin flakes. After theconcentration step, only 0.027 mg of MoS₂ flakes with thickness below 5nm remain. Based on AFM measurements, single-layer MoS₂ flakesconstitute 24% of the overall mass of MoS₂ in the concentrated solution,which implies that the mass of suspended, single-layer MoS₂ is 0.0065mg. In other words, the exfoliation yield of single-layer MoS₂ is˜0.00065%. This low exfoliation yield constitutes a remaining challengeto the field that is being actively addressed by emerging methods suchas shear mixing and ball milling. In the meantime, this low exfoliationyield further motivates the need for effective separation methods suchas DGU to isolate the minority single-layer species. After performingDGU, 0.002 mg of highly enriched single-layer MoS₂ is isolated asdetermined from optical absorbance spectroscopy and mass extinctioncoefficients that were quantified by inductively coupled plasmameasurements. The ratio of the output of enriched single-layer MoS₂(0.002 mg) to the total input single-layer MoS₂ (0.065 mg) implies a DGUyield of 30.8%.

The present teachings encompass embodiments in other specific formswithout departing from the spirit or essential characteristics thereof.The foregoing embodiments are therefore to be considered in all respectsillustrative rather than limiting on the present teachings describedherein. Scope of the present invention is thus indicated by the appendedclaims rather than by the foregoing description, and all changes thatcome within the meaning and range of equivalency of the claims areintended to be embraced therein.

We claim:
 1. A method for separating planar nanomaterials by thickness,the method comprising: centrifuging a transition metal dichalcogenidenanomaterial composition in contact with an aqueous fluid mediumcomprising a density gradient, wherein the transition metaldichalcogenide nanomaterial composition comprises one or more surfaceactive components and a polydisperse population of planar transitionmetal dichalcogenide nanomaterials which is polydisperse at least withrespect to thickness and has a mean thickness on the order ofnanometers; and separating the transition metal dichalcogenidenanomaterial composition into two or more separation fractions eachcomprising a subpopulation of planar transition metal dichalcogenidenanomaterials from the polydisperse population, wherein thesubpopulation of planar transition metal dichalcogenide nanomaterials inat least one of the two or more separation fractions has a meanthickness that is less than the mean thickness of the polydispersepopulation.
 2. The method of claim 1, wherein the planar nanomaterialscomprise MoS₂, MoSe₂, WS₂ or WSe₂ planar nanomaterials.
 3. The method ofclaim 1, wherein the one or more surface active components comprise aplanar organic group.
 4. The method of claim 3, wherein the one or moresurface active components is a copolymer of oxyethylene andoxypropylene.
 5. A method for separating transition metal dichalcogenidenanomaterials by thickness, the method comprising: sonicating transitionmetal dichalcogenide in a first fluid medium to provide a transitionmetal dichalcogenide nanomaterial composition; centrifuging thetransition metal dichalcogenide nanomaterial composition in contact withan aqueous second fluid medium comprising a density gradient, whereinthe transition metal dichalcogenide nanomaterial composition comprisesone or more surface active components and a polydisperse population ofplanar transition metal dichalcogenide nanomaterials comprisingmonolayer, bilayer, trilayer and n-layer transition metal dichalcogenidenanomaterials, where n is an integer in the range of 4 to 10; andseparating the transition metal dichalcogenide nanomaterial compositioninto two or more separation fractions each comprising a subpopulation ofplanar transition metal dichalcogenide nanomaterials from thepolydisperse population, wherein the subpopulation in at least one ofthe two or more separation fractions comprises greater than 50% of themonolayer transition metal dichalcogenide nanomaterials, bilayertransition metal dichalcogenide nanomaterials, trilayer transition metaldichalcogenide nanomaterials, or combinations thereof.
 6. The method ofclaim 5, wherein the subpopulation in at least one of the two or moreseparation fractions comprises greater than 30% of the monolayer orbilayer transition metal dichalcogenide nanomaterials, or a combinationthereof.
 7. The method of claim 5, wherein the one or more surfaceactive components comprise an amphiphilic compound having a planar core.8. The method of claim 7, wherein the one or more surface activecomponents is a copolymer of oxyethylene and oxypropylene.
 9. The methodof claim 5, wherein the planar nanomaterials comprise MoS₂, WS₂, MoSe₂or WSe₂ planar nanomaterials.
 10. The method of claim 5, wherein thetransition metal dichalcogenide is MoS₂.
 11. The method of claim 10,wherein the one or more surface active components is a copolymer ofoxyethylene and oxypropylene.
 12. The method of claim 11, wherein thesubpopulation in one of the separation fractions comprises greater than80% of the monolayer MoS₂.
 13. A method for separating monolayertransition metal dichalcogenide nanomaterials, the method comprising:centrifuging a transition metal dichalcogenide nanomaterial compositionin contact with an aqueous fluid medium comprising a density gradient,wherein the transition metal dichalcogenide nanomaterial compositioncomprises one or more copolymers of oxyethylene and oxypropylene and apolydisperse population of planar transition metal dichalcogenidenanomaterials comprising monolayer, bilayer and trilayer transitionmetal dichalcogenide nanomaterials; and separating the transition metaldichalcogenide nanomaterial composition into two or more separationfractions each comprising a subpopulation of planar transition metaldichalcogenide nanomaterials from the polydisperse population, whereinthe subpopulation in one of the two or more separation fractionscomprises greater than 50% of the monolayer transition metaldichalcogenide nanomaterials.
 14. The method of claim 13, wherein theplanar nanomaterials comprise MoS₂, WS₂, MoSe₂ or WSe₂ planarnanomaterials.
 15. The method of claim 14, wherein the subpopulation inthe one of the two or more separation fractions comprises greater than80% of the monolayer transition metal dichalcogenide nanomaterial.